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More Information: <a href="http://lussumo.com/docs">Documentation</a>, <a href="http://lussumo.com/community">Community Support</a>.</p></div> <div id="Content"><div id="NoticeCollector" class="Notices"><div class="Notice"><strong>Welcome to nForum</strong> <br />If you want to take part in these discussions either <a href="/people.php?ReturnUrl=http%3A%2F%2Fnforum.ncatlab.org%2Fdiscussion%2F1446%2F">sign in now</a> (if you have an account), <a href="https://nforum.ncatlab.org/people/?PostBackAction=ApplyForm">apply for one now</a> (if you don't).</div></div><div class="ContentInfo Top"> <h1><a href="https://nforum.ncatlab.org/5/"><a href="https://nforum.ncatlab.org/18/">nLab</a> > </a> <a href="https://nforum.ncatlab.org/5/">Latest Changes</a>: Cisinski model structure</h1> <a href="#pgbottom">Bottom of Page</a> <div class="PageInfo"> <p>1 to 28 of 28</p> <ol class="PageList PageListEmpty"> <li> </li> </ol> </div> </div> <div id="ContentBody"> <script type="text/javascript"> //<![CDATA[ function toggle_source(id) { var mysrc = document.getElementById("CommentBody_" + id).firstChild; if (mysrc.className == "source") { if (mysrc.style.display == "none") { mysrc.style.display = "block"; } else { mysrc.style.display = "none"; } } } var commentIds = new Array(0); function hide_sources() { for (i = 0; i < commentIds.length; i++) { var myself = document.getElementById("Source" + commentIds[i]); var mycmt = document.getElementById("CommentBody_" + commentIds[i]); if (mycmt.firstChild.className != "source") { myself.style.display = "none"; } } } window.onload = hide_sources; //]]> </script> <ol id="Comments"><li id="Comment_12398"> <a id="Item_1"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>1.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Jun 15th 2010</li><li><em>(edited Oct 15th 2012)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=12398#Comment_12398">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_12398"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>created [[Cisinski model structure]]</code></div><div> <p>created <a href="https://ncatlab.org/nlab/show/Cisinski model structure">Cisinski model structure</a></p> </div> </div> </li><li id="Comment_30409" class="Alternate"> <a id="Item_2"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>2.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Mar 21st 2012</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=30409#Comment_30409">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_30409"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>I have added to _[[Cisinski model structure]]_ a section _[On presheaf toposes](http://ncatlab.org/nlab/show/Cisinski+model+structure#OnPresheafToposes)_ with the essence of the definitions and statements from section 1.3 of Cisinki's book.</code></div><div> <p>I have added to <em><a href="https://ncatlab.org/nlab/show/Cisinski model structure">Cisinski model structure</a></em> a section <em><a href="http://ncatlab.org/nlab/show/Cisinski+model+structure#OnPresheafToposes">On presheaf toposes</a></em> with the essence of the definitions and statements from section 1.3 of Cisinki’s book.</p> </div> </div> </li><li id="Comment_30611"> <a id="Item_3"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>3.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Apr 3rd 2012</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=30611#Comment_30611">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_30611"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>I have been further expanding at _[[Cisinski model structrure]]_ the section _[On presheaf toposes](http://www.ncatlab.org/nlab/show/Cisinski+model+structure#OnPresheafToposes)_. Effectively I am now translating the entire chapter 1.3 of Cisinki's book and spelling out details that the book leaves out. So far I have made it through all the preliminaries up to the [main theorem](http://www.ncatlab.org/nlab/show/Cisinski+model+structure#ModelStructureFromHomotopicalStructure) stating the existence of the model structure. Next I'll try to translate / write out the full proof of that.</code></div><div> <p>I have been further expanding at <em><a href="https://ncatlab.org/nlab/show/Cisinski model structrure">Cisinski model structrure</a></em> the section <em><a href="http://www.ncatlab.org/nlab/show/Cisinski+model+structure#OnPresheafToposes">On presheaf toposes</a></em>.</p> <p>Effectively I am now translating the entire chapter 1.3 of Cisinki’s book and spelling out details that the book leaves out.</p> <p>So far I have made it through all the preliminaries up to the <a href="http://www.ncatlab.org/nlab/show/Cisinski+model+structure#ModelStructureFromHomotopicalStructure">main theorem</a> stating the existence of the model structure.</p> <p>Next I’ll try to translate / write out the full proof of that.</p> </div> </div> </li><li id="Comment_30616" class="Alternate"> <a id="Item_4"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>4.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></li> <li><span>CommentTime</span>Apr 3rd 2012</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=30616#Comment_30616">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_30616"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Thank you! I'm sure this will be a great thing to have.</code></div><div> <p>Thank you! I’m sure this will be a great thing to have.</p> </div> </div> </li><li id="Comment_30626"> <a id="Item_5"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>5.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Apr 4th 2012</li><li><em>(edited Apr 4th 2012)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=30626#Comment_30626">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_30626"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Good to hear that you find this useful. Right now I need these notes as a script for a seminar talk where I will present the proof -- or at least a good bit of it... This morning, I have added a few more bits. The main new aspect for any potential reader is that I have added much more structure to the flow of the argument, see the new section outline at _[[Cisinki model structure]]_ and the outline of the proof of the main theorem _[here](http://ncatlab.org/nlab/show/Cisinski+model+structure#ModelStructureFromHomotopicalStructure)_. (Where "main theorem" still means "main theorem of section 1.3", mind you.) The main remaining gap as far as details for the proofs go is currently the [last section](http://ncatlab.org/nlab/show/Cisinski+model+structure#AcyclicCofibrationFollowedByFibration). I'll try to take care of that now.</code></div><div> <p>Good to hear that you find this useful. Right now I need these notes as a script for a seminar talk where I will present the proof – or at least a good bit of it…</p> <p>This morning, I have added a few more bits. The main new aspect for any potential reader is that I have added much more structure to the flow of the argument, see the new section outline at <em><a href="https://ncatlab.org/nlab/show/Cisinki model structure">Cisinki model structure</a></em> and the outline of the proof of the main theorem <em><a href="http://ncatlab.org/nlab/show/Cisinski+model+structure#ModelStructureFromHomotopicalStructure">here</a></em>. (Where “main theorem” still means “main theorem of section 1.3”, mind you.)</p> <p>The main remaining gap as far as details for the proofs go is currently the <a href="http://ncatlab.org/nlab/show/Cisinski+model+structure#AcyclicCofibrationFollowedByFibration">last section</a>. I’ll try to take care of that now.</p> </div> </div> </li><li id="Comment_30764" class="Alternate"> <a id="Item_6"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>6.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Apr 17th 2012</li><li><em>(edited Apr 17th 2012)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=30764#Comment_30764">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_30764"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Added to _[[Cisinski model structure]]_ a handful of items on "localizers" on presheaf categories, _[here](http://ncatlab.org/nlab/show/Cisinski+model+structure#ALocalizers)_</code></div><div> <p>Added to <em><a href="https://ncatlab.org/nlab/show/Cisinski model structure">Cisinski model structure</a></em> a handful of items on “localizers” on presheaf categories, <em><a href="http://ncatlab.org/nlab/show/Cisinski+model+structure#ALocalizers">here</a></em></p> </div> </div> </li><li id="Comment_35994"> <a id="Item_7"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>7.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/4/">Urs</a></li> <li><span>CommentTime</span>Oct 15th 2012</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=35994#Comment_35994">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_35994"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/4/">Urs</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>added the remark that every Cisinski model structure is in particular [[combinatorial model structure|combinatorial]] (and added an Examples-link the other way round).</code></div><div> <p>added the remark that every Cisinski model structure is in particular <a href="https://ncatlab.org/nlab/show/combinatorial model structure">combinatorial</a> (and added an Examples-link the other way round).</p> </div> </div> </li><li id="Comment_64699" class="Alternate"> <a id="Item_8"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>8.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/356/">Dmitri Pavlov</a></li> <li><span>CommentTime</span>Aug 2nd 2017</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=64699#Comment_64699">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_64699"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/356/">Dmitri Pavlov</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Can we describe the ∞-category underlying a Cisinski model structure in terms of its topos and localizer? As far as I understand, for a nonempty localizer the Cisinski model structure is the left Bousfield localization of the Cisinski model structure with the empty localizer at the morphisms in the localizer, which has an obvious ∞-categorical translation in terms of (reflective) localizations. However, what is the ∞-categorical meaning of the Cisinski model structure with the empty localizer? Staring at the examples it seems to me that for toposes of presheaves the underlying ∞-category should be just the ∞-category of ∞-presheaves. And for arbitrary toposes one can expect to get some version of ∞-sheaves, hypercompleted or not.</code></div><div> <p>Can we describe the ∞-category underlying a Cisinski model structure in terms of its topos and localizer?</p> <p>As far as I understand, for a nonempty localizer the Cisinski model structure is the left Bousfield localization of the Cisinski model structure with the empty localizer at the morphisms in the localizer, which has an obvious ∞-categorical translation in terms of (reflective) localizations.</p> <p>However, what is the ∞-categorical meaning of the Cisinski model structure with the empty localizer?</p> <p>Staring at the examples it seems to me that for toposes of presheaves the underlying ∞-category should be just the ∞-category of ∞-presheaves. And for arbitrary toposes one can expect to get some version of ∞-sheaves, hypercompleted or not.</p> </div> </div> </li><li id="Comment_73699"> <a id="Item_9"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>9.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></li> <li><span>CommentTime</span>Nov 5th 2018</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=73699#Comment_73699">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_73699"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Finish proof of [Cisinski 06, lemma 1.3.34], already started in the previous edit whithout comment, now only correcting typos. Gábor Braun <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/44">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/44">v44</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Finish proof of [Cisinski 06, lemma 1.3.34], already started in the previous edit whithout comment, now only correcting typos.</p> <p>Gábor Braun</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/44">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/44">v44</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_76095" class="Alternate"> <a id="Item_10"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>10.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></li> <li><span>CommentTime</span>Feb 16th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76095#Comment_76095">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76095"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>The statement at [[Cisinski model structure]] about cellular models (proposition 2.34 on the page, prop. 1.2.27 in Cisinski 06) refers to *presheaf* toposes. However, it seems to me that the same fact should be true about arbitrary Grothendieck toposes (that the monomorphisms are cofibrantly generated by a set), by essentially the same proof using the sheafified representables instead of the ordinary representables. Is this true, and if so is it written down anywhere?</code></div><div> <p>The statement at <a href="https://ncatlab.org/nlab/show/Cisinski model structure">Cisinski model structure</a> about cellular models (proposition 2.34 on the page, prop. 1.2.27 in Cisinski 06) refers to <em>presheaf</em> toposes. However, it seems to me that the same fact should be true about arbitrary Grothendieck toposes (that the monomorphisms are cofibrantly generated by a set), by essentially the same proof using the sheafified representables instead of the ordinary representables. Is this true, and if so is it written down anywhere?</p> </div> </div> </li><li id="Comment_76096"> <a id="Item_11"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>11.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/822/">Richard Williamson</a></li> <li><span>CommentTime</span>Feb 16th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76096#Comment_76096">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76096"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/822/">Richard Williamson</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Just a quick note that Cisinski generalised some of his work to topoi in [this unpublished work](http://www.mathematik.uni-regensburg.de/cisinski/mtest2.pdf), but it’s a long time since I’ve looked at it, and I don’t know if what you are looking for is in there.</code></div><div> <p>Just a quick note that Cisinski generalised some of his work to topoi in <a href="http://www.mathematik.uni-regensburg.de/cisinski/mtest2.pdf">this unpublished work</a>, but it’s a long time since I’ve looked at it, and I don’t know if what you are looking for is in there.</p> </div> </div> </li><li id="Comment_76099" class="Alternate"> <a id="Item_12"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>12.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></li> <li><span>CommentTime</span>Feb 16th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76099#Comment_76099">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76099"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Thanks! It's stated there as Prop. 1.2.2, without proof (but, as I said, I think the proof in Cisinski 06 generalizes without trouble).</code></div><div> <p>Thanks! It’s stated there as Prop. 1.2.2, without proof (but, as I said, I think the proof in Cisinski 06 generalizes without trouble).</p> </div> </div> </li><li id="Comment_76100"> <a id="Item_13"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>13.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></li> <li><span>CommentTime</span>Feb 16th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76100#Comment_76100">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76100"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Added that unpublished reference to the page. <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/47">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/47">v47</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Added that unpublished reference to the page.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/47">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/47">v47</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_76109" class="Alternate"> <a id="Item_14"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>14.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/822/">Richard Williamson</a></li> <li><span>CommentTime</span>Feb 16th 2019</li><li><em>(edited Feb 16th 2019)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76109#Comment_76109">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76109"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/822/">Richard Williamson</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Great! Yes, at the beginning of section 2, the second sentence translates to something like: "We have omitted those proofs already given in the setting of presheaf categories which can be given mutatis mutandis in that of sheaf categories, referring the reader to [Cisinski's book]".</code></div><div> <p>Great! Yes, at the beginning of section 2, the second sentence translates to something like:</p> <p>“We have omitted those proofs already given in the setting of presheaf categories which can be given mutatis mutandis in that of sheaf categories, referring the reader to [Cisinski’s book]”.</p> </div> </div> </li><li id="Comment_76115"> <a id="Item_15"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>15.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></li> <li><span>CommentTime</span>Feb 17th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76115#Comment_76115">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76115"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Thanks! My French isn't quite good enough for that to have jumped out at me. (-:O</code></div><div> <p>Thanks! My French isn’t quite good enough for that to have jumped out at me. (-:O</p> </div> </div> </li><li id="Comment_76148" class="Alternate"> <a id="Item_16"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>16.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/822/">Richard Williamson</a></li> <li><span>CommentTime</span>Feb 17th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76148#Comment_76148">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76148"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/822/">Richard Williamson</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Added definition of homotopical datum (donnée homotopique), which seemed to be missing. Gave the example of the [[minimal Cisinski model structure]] on any presheaf category. Left the latter as a page to be created. <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/48">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/48">v48</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Added definition of homotopical datum (donnée homotopique), which seemed to be missing. Gave the example of the <a href="https://ncatlab.org/nlab/show/minimal Cisinski model structure">minimal Cisinski model structure</a> on any presheaf category. Left the latter as a page to be created.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/48">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/48">v48</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_76162"> <a id="Item_17"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>17.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/94/">Marc</a></li> <li><span>CommentTime</span>Feb 18th 2019</li><li><em>(edited Feb 18th 2019)</em></li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76162#Comment_76162">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76162"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/94/">Marc</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>The case of Grothendieck abelian categories and Grothendieck toposes is also treated in Prop. 1.12 in Tibor Beke's paper <https://faculty.uml.edu/tbeke/sheafi.pdf></code></div><div> <p>The case of Grothendieck abelian categories and Grothendieck toposes is also treated in Prop. 1.12 in Tibor Beke’s paper <a href="https://faculty.uml.edu/tbeke/sheafi.pdf">https://faculty.uml.edu/tbeke/sheafi.pdf</a></p> </div> </div> </li><li id="Comment_76164" class="Alternate"> <a id="Item_18"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>18.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></li> <li><span>CommentTime</span>Feb 18th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76164#Comment_76164">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76164"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/3/">Mike Shulman</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Thanks! I've added this to [[cellular model]] too.</code></div><div> <p>Thanks! I’ve added this to <a href="https://ncatlab.org/nlab/show/cellular model">cellular model</a> too.</p> </div> </div> </li><li id="Comment_76914"> <a id="Item_19"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>19.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/6/">Tim_Porter</a></li> <li><span>CommentTime</span>Mar 28th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76914#Comment_76914">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76914"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/6/">Tim_Porter</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Fixed a typo <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/49">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/49">v49</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Fixed a typo</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/49">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/49">v49</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_76915" class="Alternate"> <a id="Item_20"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>20.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/6/">Tim_Porter</a></li> <li><span>CommentTime</span>Mar 28th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76915#Comment_76915">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76915"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/6/">Tim_Porter</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Lightened the wording. <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/49">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/49">v49</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Lightened the wording.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/49">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/49">v49</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_76916"> <a id="Item_21"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>21.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/6/">Tim_Porter</a></li> <li><span>CommentTime</span>Mar 28th 2019</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=76916#Comment_76916">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_76916"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/6/">Tim_Porter</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Added a short ideas section. <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/49">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/49">v49</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Added a short ideas section.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/49">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/49">v49</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_83848" class="Alternate"> <a id="Item_22"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>22.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></li> <li><span>CommentTime</span>Apr 15th 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=83848#Comment_83848">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_83848"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Prefaced the "Cofibration followed by an acyclic fibration" with the elementary construction of functoral factorization via partial map classifier. <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/50">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/50">v50</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Prefaced the “Cofibration followed by an acyclic fibration” with the elementary construction of functoral factorization via partial map classifier.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/50">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/50">v50</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_83849"> <a id="Item_23"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>23.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></li> <li><span>CommentTime</span>Apr 15th 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=83849#Comment_83849">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_83849"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Expanded on the "minimal Cisinski model structure" to include the description of the generating acyclic cofibrations. <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/50">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/50">v50</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Expanded on the “minimal Cisinski model structure” to include the description of the generating acyclic cofibrations.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/50">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/50">v50</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_84127" class="Alternate"> <a id="Item_24"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>24.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></li> <li><span>CommentTime</span>Apr 25th 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=84127#Comment_84127">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_84127"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>In the description of the minimal Cisinski model structure, changed "generating acyclic cofibration" to "generating anodyne extension". <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/51">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/51">v51</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>In the description of the minimal Cisinski model structure, changed “generating acyclic cofibration” to “generating anodyne extension”.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/51">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/51">v51</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_87944"> <a id="Item_25"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>25.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></li> <li><span>CommentTime</span>Nov 22nd 2020</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=87944#Comment_87944">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_87944"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Corrected the description of the minimal Cisinski model structure. <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/53">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/53">v53</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Corrected the description of the minimal Cisinski model structure.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/53">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/53">v53</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_88840" class="Alternate"> <a id="Item_26"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>26.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></li> <li><span>CommentTime</span>Jan 5th 2021</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=88840#Comment_88840">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_88840"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Added a reference to Cisinski's 2020 book. <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/54">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/54">v54</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Added a reference to Cisinski’s 2020 book.</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/54">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/54">v54</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_106129"> <a id="Item_27"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>27.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></li> <li><span>CommentTime</span>Jan 6th 2023</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=106129#Comment_106129">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_106129"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1691/">nLab edit announcer</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Fixed reference to wrong chapter Anonymous <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/61">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/61">v61</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Fixed reference to wrong chapter</p> <p>Anonymous</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/61">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/61">v61</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li><li id="Comment_110551" class="Alternate"> <a id="Item_28"></a> <div class="CommentHeader"> <ul> <li><span>CommentRowNumber</span>28.</li><li><span>CommentAuthor</span><a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></li> <li><span>CommentTime</span>Jun 10th 2023</li></ul></div> <div class="CommentActions"> <div class="CommentActionsInner"><ul class="CommentActionsList"><li><a href="https://nforum.ncatlab.org/discussion/1446/cisinski-model-structure/?Focus=110551#Comment_110551">PermaLink</a></li></ul></div></div><div class="CommentBody" id="CommentBody_110551"><div class="source" style="display: none;"><span class="sourceType">Author: <a href="https://nforum.ncatlab.org/account/1623/">Hurkyl</a></span><br/><span class="sourceType">Format: MarkdownItex</span><code>Added some links to lawvere cylinder <a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/62">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/62">v62</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></code></div><div> <p>Added some links to lawvere cylinder</p> <p><a href="https://ncatlab.org/nlab/revision/diff/Cisinski+model+structure/62">diff</a>, <a href="https://ncatlab.org/nlab/revision/Cisinski+model+structure/62">v62</a>, <a href="https://ncatlab.org/nlab/show/Cisinski+model+structure">current</a></p> </div> </div> </li></ol> </div><div class="ContentInfo Middle"> <div class="PageInfo"> <p>1 to 28 of 28</p> <ol class="PageList PageListEmpty"> <li> </li> </ol> </div> </div></div> <a id="pgbottom" > </a> </div> </div></body> </html>