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width: 0.3em;"></span> <a href="/nlab/show/diff/HomePage" accesskey="H" title="Home page">Home Page</a> | <a href="/nlab/all_pages" accesskey="A" title="List of all pages">All Pages</a> | <a href="/nlab/latest_revisions" accesskey="U" title="Latest edits and page creations">Latest Revisions</a> | <a href="https://nforum.ncatlab.org/discussion/10607/#Item_7" title="Discuss this page in its dedicated thread on the nForum" style="color: black">Discuss this page</a> | <a href="/nlab/author/Andr%C3%A9+Joyal" style="color: black" title="Overview of nLab pages which André Joyal has edited">Pages contributed to</a> <form accept-charset="utf-8" action="/nlab/search" id="navigationSearchForm" method="get"> <fieldset class="search"><input type="text" id="searchField" name="query" value="Search" style="display:inline-block; float: left;" onfocus="this.value == 'Search' ? this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> <span id='navEnd'></span> </div> <div id="revision"> <p class="show_diff"> Showing changes from revision #43 to #44: <ins class="diffins">Added</ins> | <del class="diffdel">Removed</del> | <del class="diffmod">Chan</del><ins class="diffmod">ged</ins> </p> <p>André Joyal is a Canadian mathematician, a professor at Université du Québec à Montréal.</p> <p>He got his PhD in <a href='https://web.archive.org/web/20060325080542/http://132.208.138.87/_joyal/'>1971</a> from Université de Montréal.</p> <p>His wide mathematical work, is mainly in <a class='existingWikiWord' href='/nlab/show/diff/category+theory'>category theory</a>, <a class='existingWikiWord' href='/nlab/show/diff/sheaf+and+topos+theory'>topos theory</a> and abstract <a class='existingWikiWord' href='/nlab/show/diff/homotopy+theory'>homotopy theory</a>. His works include a wide generalization of <a class='existingWikiWord' href='/nlab/show/diff/Galois+theory'>Galois theory</a> with <a class='existingWikiWord' href='/nlab/show/diff/Myles+Tierney'>Myles Tierney</a>, the combinatorial ideas of “Joyal’s <a class='existingWikiWord' href='/nlab/show/diff/species'>species</a>”, discovery of the category structure on the collection of Conway combinatorial <a class='existingWikiWord' href='/nlab/show/diff/game+theory'>games</a>, the discovery of Kripke-Joyal semantics, a series of works (mainly with <a class='existingWikiWord' href='/nlab/show/diff/Ross+Street'>Ross Street</a><span> ) about<del class='diffmod'> (braided,</del><ins class='diffmod'> (</ins><del class='diffdel'> tortile</del><del class='diffdel'> etc.)</del></span><ins class='diffins'><a class='existingWikiWord' href='/nlab/show/diff/braided+monoidal+category'>braided</a></ins><ins class='diffins'>, </ins><ins class='diffins'><a class='existingWikiWord' href='/nlab/show/diff/ribbon+category'>tortile</a></ins><ins class='diffins'> etc.) </ins><a class='existingWikiWord' href='/nlab/show/diff/monoidal+category'>monoidal categories</a> prompted partly by methods and motivation in theoretical physics, much of his work for about last 30 years centered on developing the theory of <a class='existingWikiWord' href='/nlab/show/diff/quasi-category'>quasicategories</a>, after the first ideas of Boardman and Vogt. In the 1980s Joyal invented a Quillen <a class='existingWikiWord' href='/nlab/show/diff/model+category'>model category</a> <a class='existingWikiWord' href='/nlab/show/diff/model+structure+for+quasi-categories'>structure on the category of simplicial sets</a> (and <a class='existingWikiWord' href='/nlab/show/diff/model+structure+on+simplicial+presheaves'>categories of simplicial presheaves</a>). Joyal and J. Kock more recently proved <a class='existingWikiWord' href='/nlab/show/diff/Simpson%27s+conjecture'>Simpson's conjecture</a> (on higher categories via weak units) in categorical dimension 3.</p> <p>Joyal promoted <a class='existingWikiWord' href='/nlab/show/diff/quasi-category'>quasi-categories</a>, greatly extending their theory, as a basis for <a class='existingWikiWord' href='/nlab/show/diff/%28infinity%2C1%29-category+theory'>(∞,1)-category theory</a>.</p> <p>Joyal has contributed to the <math class='maruku-mathml' display='inline' id='mathml_c8d7fb2a1bb07c161d002d3c11faf536574b9a90_1' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mi>n</mi></mrow><annotation encoding='application/x-tex'>n</annotation></semantics></math>Lab as ‘joyal’; he once began a project at <a class='existingWikiWord' href='/joyalscatlab/published/HomePage' title='joyalscatlab'>joyalscatlab</a>.</p> <p><a href='http://professeurs.uqam.ca/professeur?c=joyal.andre'>webpage</a>, <a href='http://en.wikipedia.org/wiki/Andr%C3%A9_Joyal'>wikipedia</a></p> <p><a href='https://web.archive.org/web/19990221035246/http://www.math.uqam.ca/_joyal/'>Old webpage</a>.</p> <p><a href='https://web.archive.org/web/20030707225620/http://132.208.138.87/_joyal/joyal.pdf'>CV</a> from 1995.</p> <h2 id='selected_writings'>Selected writings</h2> <p>On <a class='existingWikiWord' href='/nlab/show/diff/forcing'>forcing</a> via <a class='existingWikiWord' href='/nlab/show/diff/classifying+topos'>classifying toposes</a> and the <a class='existingWikiWord' href='/nlab/show/diff/classifying+topos+of+a+localic+groupoid'>classifying topos of a localic groupoid</a>:</p> <ul> <li id='JoyalTierney84'> <p><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Myles+Tierney'>Myles Tierney</a>, <em>An extension of the Galois theory of Grothendieck</em>, Mem. Amer. Math. Soc. <strong>309</strong> (1984) [[ISBN:978-1-4704-0722-3](https://bookstore.ams.org/memo-51-309)]</p> <del class='diffmod'><p>(historical note: according to MR756176 (86d:18002) by <a class='existingWikiWord' href='/nlab/show/diff/Peter+Johnstone'>Peter Johnstone</a>, the main results of this monograph were obtained by the authors around 1978-1979, typed version circulated from 1982, and the results influenced the field much before the actual publication)</p></del><ins class='diffmod'><blockquote> <p>(historical note: according to MR756176 (86d:18002) by <a class='existingWikiWord' href='/nlab/show/diff/Peter+Johnstone'>Peter Johnstone</a>, the main results of this monograph were obtained by the authors around 1978-1979, the typed version circulated from 1982, and the results influenced the field much before the actual publication)</p> </blockquote></ins> </li> </ul> <ins class='diffins'><p>Introducing the notion of <a class='existingWikiWord' href='/nlab/show/diff/braided+monoidal+category'>braided monoidal categories</a>:</p></ins><ins class='diffins'> </ins><ins class='diffins'><ul> <li id='JoyalStreet85'> <p><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Ross+Street'>Ross Street</a>: <em>Braided monoidal categories</em>, <em>Macquarie Math Reports</em> <strong>85-0067</strong> (1985) [[pdf](http://web.science.mq.edu.au/~street/BMC850067.pdf), <a class='existingWikiWord' href='/nlab/files/JoyalStreet-BraidedMonoidal85.pdf' title='pdf'>pdf</a>]</p> </li> <li id='JoyalStreet86'> <p><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Ross+Street'>Ross Street</a>: <em>Braided monoidal categories</em>, <em>Macquarie Math Reports</em> <strong>860081</strong> (1986) [[pdf](http://maths.mq.edu.au/~street/JS1.pdf), <a class='existingWikiWord' href='/nlab/files/JoyalStreet-BraidedMonoidal.pdf' title='pdf'>pdf</a>]</p> </li> <li> <p><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Ross+Street'>Ross Street</a>, <em>Braided tensor categories</em>, Adv. Math. <strong>102</strong> (1993) 20-78 [[doi:10.1006/aima.1993.1055](https://doi.org/10.1006/aima.1993.1055)]</p> </li> </ul></ins><ins class='diffins'> </ins><p>On <a class='existingWikiWord' href='/nlab/show/diff/algebraic+set+theory'>algebraic set theory</a>:</p> <ul> <li>A. Joyal, <a class='existingWikiWord' href='/nlab/show/diff/Ieke+Moerdijk'>I. Moerdijk</a>, <em>Algebraic set theory</em>. London Mathematical Society Lecture Note Series <strong>220</strong>. Cambridge Univ. Press (1995) viii+123 pp. ISBN: 0-521-55830-1</li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/transition+system'>transition systems</a>, <a class='existingWikiWord' href='/nlab/show/diff/bisimulation'>bisimulations</a> and <a class='existingWikiWord' href='/nlab/show/diff/open+morphism'>open morphisms</a>:</p> <ul> <li id='JoyalNielsenWisnkel94'><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Mogens+Nielsen'>Mogens Nielsen</a>, <a class='existingWikiWord' href='/nlab/show/diff/Glynn+Winskel'>Glynn Winskel</a>: <em>Bisimulation from open maps</em>, BRICS report series RS-94-7 (1994) [[doi:10.7146/brics.v1i7.21663](https://doi.org/10.7146/brics.v1i7.21663), <a href='http://www.brics.dk/RS/94/7/BRICS-RS-94-7.pdf'>pdf</a>], Information and Computation <strong>127</strong> 2 (1996) 164-185 [[doi:10.1006/inco.1996.0057](https://doi.org/10.1006/inco.1996.0057)]</li> </ul> <p>Introducing the notion of <a class='existingWikiWord' href='/nlab/show/diff/traced+monoidal+category'>traced monoidal categories</a>:</p> <ul> <li id='JoyalStreetVerity96'><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Ross+Street'>Ross Street</a>, <a class='existingWikiWord' href='/nlab/show/diff/Dominic+Verity'>Dominic Verity</a>, <em>Traced monoidal categories</em>, Math. Proc. Camb. Phil. Soc. <strong>119</strong> (1996) 447-468 [[pdf](http://sci-prew.inf.ua/v119/3/S0305004100074338.pdf), <a href='https://doi.org/10.1017/S0305004100074338'>doi:10.1017/S0305004100074338</a>]</li> </ul> <p>On the <a class='existingWikiWord' href='/nlab/show/diff/Dwyer-Kan+fundamental+simplicial+groupoid'>Dwyer-Kan loop groupoid</a>-construction (<a class='existingWikiWord' href='/nlab/show/diff/path+groupoid'>path</a>-<a class='existingWikiWord' href='/nlab/show/diff/simplicial+groupoid'>simplicial groupoids</a>):</p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Myles+Tierney'>Myles Tierney</a>, <em>On the theory of path groupoids</em>, Journal of Pure and Applied Algebra <strong>149</strong> 1 (2000) 69-100 []</li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/quasi-category'>quasi-categories</a>:</p> <ul> <li><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <em>Quasi-categories and Kan complexes</em>, J. Pure Appl. Algebra <strong>175</strong> (2002) 207-222 (special volume celebrating the 70th birthday of Prof. Max Kelly) []</li> </ul> <p>On the <a class='existingWikiWord' href='/nlab/show/diff/Quillen+equivalence'>Quillen equivalence</a> between the <a class='existingWikiWord' href='/nlab/show/diff/model+category'>model categories</a> for <a class='existingWikiWord' href='/nlab/show/diff/quasi-category'>quasi-categories</a> and <a class='existingWikiWord' href='/nlab/show/diff/complete+Segal+space'>complete Segal spaces</a>:</p> <ul> <li id='JoyalTierney07'><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>Andre Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Myles+Tierney'>Myles Tierney</a>, <em>Quasi-categories vs. Segal spaces</em>, in <em>Categories in Algebra, Geometry and Mathematical Physics</em>, Contemporary Mathematics <strong>431</strong> (2007) [[arXiv:math/0607820](http://arxiv.org/abs/math/0607820), <a href='https://doi.org/10.1090/conm/431'>doi:10.1090/conm/431</a>]</li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/quasi-category'>quasi-categories</a>:</p> <ul> <li id='Joyal08'><del class='diffmod'><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a></del><ins class='diffmod'> </ins><del class='diffmod'>, </del><ins class='diffmod'><p><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <em>Notes on quasi-categories</em> (2008) [[pdf](http://www.math.uchicago.edu/~may/IMA/Joyal.pdf), <a class='existingWikiWord' href='/nlab/files/JoyalNotesOnQuasiCategories.pdf' title='pdf'>pdf</a>]</p></ins><del class='diffmod'><em><a class='existingWikiWord' href='/nlab/show/diff/The+Theory+of+Quasi-Categories+and+its+Applications'>The Theory of Quasi-Categories and its Applications</a></em></del><ins class='diffmod'> </ins><del class='diffdel'>, lectures at </del><del class='diffdel'><em><a href='https://lists.lehigh.edu/pipermail/algtop-l/2007q4/000017.html'>Advanced Course on Simplicial Methods in Higher Categories</a></em></del><del class='diffdel'>, CRM 2008 (</del><del class='diffdel'><a href='http://mat.uab.cat/~kock/crm/hocat/advanced-course/Quadern45-2.pdf'>pdf</a></del><del class='diffdel'>, </del><del class='diffdel'><a class='existingWikiWord' href='/nlab/files/JoyalTheoryOfQuasiCategories.pdf' title='pdf'>pdf</a></del><del class='diffdel'>)</del></li><ins class='diffins'> </ins><ins class='diffins'><li id='Joyal08'> <p><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <em><a class='existingWikiWord' href='/nlab/show/diff/The+Theory+of+Quasi-Categories+and+its+Applications'>The Theory of Quasi-Categories and its Applications</a></em>, lectures at <em><a href='https://lists.lehigh.edu/pipermail/algtop-l/2007q4/000017.html'>Advanced Course on Simplicial Methods in Higher Categories</a></em>, CRM 2008 (<a href='http://mat.uab.cat/~kock/crm/hocat/advanced-course/Quadern45-2.pdf'>pdf</a>, <a class='existingWikiWord' href='/nlab/files/JoyalTheoryOfQuasiCategories.pdf' title='pdf'>pdf</a>)</p> </li></ins> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/simplicial+homotopy+theory'>simplicial homotopy theory</a>, the <a class='existingWikiWord' href='/nlab/show/diff/classical+model+structure+on+simplicial+sets'>classical model structure on simplicial sets</a> and the <a class='existingWikiWord' href='/nlab/show/diff/classical+model+structure+on+topological+spaces'>classical model structure on topological spaces</a>:</p> <ul> <li id='JoyalTierney08'> <p><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Myles+Tierney'>Myles Tierney</a> <em>Notes on simplicial homotopy theory</em>, Lecture at <em><a href='https://lists.lehigh.edu/pipermail/algtop-l/2007q4/000017.html'>Advanced Course on Simplicial Methods in Higher Categories</a></em>, CRM 2008 (<a class='existingWikiWord' href='/nlab/files/JoyalTierneyNotesOnSimplicialHomotopyTheory.pdf' title='pdf'>pdf</a>)</p> </li> <li id='JoyalTierney09'> <p><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <a class='existingWikiWord' href='/nlab/show/diff/Myles+Tierney'>Myles Tierney</a> <em>An introduction to simplicial homotopy theory</em>, 2009 (<a href='http://hopf.math.purdue.edu/cgi-bin/generate?/Joyal-Tierney/JT-chap-01'>web</a>, <a class='existingWikiWord' href='/nlab/files/JoyalTierneySimplicialHomotopyTheory.pdf' title='pdf'>pdf</a>)</p> </li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/homotopy+theory'>homotopy theory</a> via <a class='existingWikiWord' href='/nlab/show/diff/category+theory'>category theory</a>:</p> <ul> <li id='JoyalCategorialHoTT'><a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <em><a class='existingWikiWord' href='/nlab/files/Categorical+Homotopy+Type+Theory.pdf' title='Categorical Homotopy Type Theory'>Categorical Homotopy Type Theory</a></em>, MIT Topology Seminar (March 17, 2014)</li> </ul> <p>Proving the <a class='existingWikiWord' href='/nlab/show/diff/Blakers-Massey+theorem'>Blakers-Massey theorem</a> in any <a class='existingWikiWord' href='/nlab/show/diff/%28infinity%2C1%29-topos'>$(\infty,1)$-topos</a> and with the <a class='existingWikiWord' href='/nlab/show/diff/%28n-connected%2C+n-truncated%29+factorization+system'>(n-connected, n-truncated) factorization system</a> allowed to be replaced by more general <a class='existingWikiWord' href='/nlab/show/diff/modal+homotopy+type+theory'>modalities</a>:</p> <ul> <li id='AnelBiedermanFinsterJoyal17a'><a class='existingWikiWord' href='/nlab/show/diff/Mathieu+Anel'>Mathieu Anel</a>, <a class='existingWikiWord' href='/nlab/show/diff/Georg+Biedermann'>Georg Biedermann</a>, <a class='existingWikiWord' href='/nlab/show/diff/Eric+Finster'>Eric Finster</a>, <a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <em>A Generalized Blakers-Massey Theorem</em>, Journal of Topology <strong>13</strong> 4 (2020) 1521-1553 <math class='maruku-mathml' display='inline' id='mathml_c8d7fb2a1bb07c161d002d3c11faf536574b9a90_2' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mo stretchy='false'>[</mo></mrow><annotation encoding='application/x-tex'>[</annotation></semantics></math><a href='https://arxiv.org/abs/1703.09050'>arXiv:1703.09050</a>, <a href='https://doi.org/10.1112/topo.12163'>doi:10.1112/topo.12163</a><math class='maruku-mathml' display='inline' id='mathml_c8d7fb2a1bb07c161d002d3c11faf536574b9a90_3' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mo stretchy='false'>]</mo></mrow><annotation encoding='application/x-tex'>]</annotation></semantics></math></li> </ul> <p>On <a class='existingWikiWord' href='/nlab/show/diff/%28infinity%2C1%29-topos'>$(\infty,1)$-toposes</a> understood as <em><a class='existingWikiWord' href='/nlab/show/diff/logos'>logoi</a></em>:</p> <ul> <li id='AnelJoyal19'><a class='existingWikiWord' href='/nlab/show/diff/Mathieu+Anel'>Mathieu Anel</a>, <a class='existingWikiWord' href='/nlab/show/diff/Andr%C3%A9+Joyal'>André Joyal</a>, <em>Topo-logie</em>, in <em><a class='existingWikiWord' href='/nlab/show/diff/New+Spaces+for+Mathematics+and+Physics'>New Spaces for Mathematics and Physics</a></em>, Cambridge University Press (2021) 155-257 [[doi:10.1017/9781108854429.007](https://doi.org/10.1017/9781108854429.007), <a href='http://mathieu.anel.free.fr/mat/doc/Anel-Joyal-Topo-logie.pdf'>pdf</a>]</li> </ul> <p>See also:</p> <ul> <li> <p>A. Joyal, M. Tierney, <em>Quasi-categories vs Segal spaces</em>, Categories in algebra, geometry and mathematical physics, 277–326, Contemp. Math. <strong>431</strong>, Amer. Math. Soc., Providence, RI, 2007. <a href='http://arxiv.org/abs/math.AT/0607820'>math.AT/0607820</a>.</p> </li> <li> <p>A. Joyal, M. Tierney, <em>On the theory of path groupoids</em>, J. Pure Appl. Algebra <strong>149</strong> (2000), no. 1, 69–100, <a href='http://dx.doi.org/10.1016/S0022-4049%2898%2900164-9'>doi</a></p> </li> <li> <p>A. Joyal, R. Street, <em>Pullbacks equivalent to pseudopullbacks</em>, Cahiers topologie et géométrie différentielle catégoriques 34 (1993) 153-156; <a href='http://www.numdam.org/item?id=CTGDC_1993__34_2_153_0'>numdam</a> MR94a:18004.</p> </li> <li> <p>A. Joyal, M. Tierney, <em>Strong stacks and classifying spaces</em>, Category theory (Como, 1990), 213–236, Lecture Notes in Math. <strong>1488</strong>, Springer 1991.</p> </li> <li> <p>A. Joyal, <a class='existingWikiWord' href='/nlab/show/diff/Ross+Street'>R. Street</a>, <em>An introduction to Tannaka duality and quantum groups</em>, Category theory (Como, 1990), 413–492, Lecture Notes in Math. <strong>1488</strong>, Springer 1991 (<a href='http://www.math.mq.edu.au/~street/CT90Como.pdf'>pdf</a>).</p> </li> <li> <p>A. Joyal, R. Street, <em>The geometry of tensor calculus I</em>, Adv. Math. <strong>88</strong>(1991), no. 1, 55–112, <a href='http://dx.doi.org/10.1016/0001-8708%2891%2990003-P'>doi</a>; <em>Tortile Yang-Baxter operators in tensor categories</em>, J. Pure Appl. Algebra <strong>71</strong> (1991), no. 1, 43–51, <a href='http://dx.doi.org/10.1016/0022-4049%2891%2990039-5'>doi</a><span> ;</span><del class='diffdel'><em>Braided tensor categories</em></del><del class='diffdel'>, Adv. Math. </del><del class='diffdel'><strong>102</strong></del><del class='diffdel'> (1993), no. 1, 20–78, </del><del class='diffdel'><a href='http://dx.doi.org/10.1006/aima.1993.1055'>doi</a></del><del class='diffdel'>.</del></p> </li> <del class='diffdel'><li> <p>A. Joyal, R. Street, <em>Braided monoidal categories</em>, Macquarie Math Reports 860081 (1986) <a href='http://www.maths.mq.edu.au/~street/JS1.pdf'>pdf</a>; Macquarie Math Reports 850067 (1985) <a href='http://www.math.mq.edu.au/~street/BMC850067.pdf'>pdf</a>.</p> </li></del><del class='diffdel'> </del><del class='diffdel'><li> <p>A Joyal, <em>Notes on quasicategories</em>, (<a href='http://www.math.uchicago.edu/~may/IMA/Joyal.pdf'>draft</a>)</p> </li></del><del class='diffdel'> </del><li> <p>A. Joyal, Letter to <a class='existingWikiWord' href='/nlab/show/diff/Alexander+Grothendieck'>Alexander Grothendieck</a>, 11.4.1984, <a class='existingWikiWord' href='/nlab/files/lettrejoyal.pdf' title='Lettre d'Andre Joyal a Alexandre Grothendieck'>Lettre d'Andre Joyal a Alexandre Grothendieck</a>.</p> </li> <li> <p>A. Joyal, <em>Disks, duality and <math class='maruku-mathml' display='inline' id='mathml_c8d7fb2a1bb07c161d002d3c11faf536574b9a90_4' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mi>Θ</mi></mrow><annotation encoding='application/x-tex'>\Theta</annotation></semantics></math>-categories</em>, preprint (1997) (contains an original definition of a weak <math class='maruku-mathml' display='inline' id='mathml_c8d7fb2a1bb07c161d002d3c11faf536574b9a90_5' xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow><mi>n</mi></mrow><annotation encoding='application/x-tex'>n</annotation></semantics></math>-category: for a short account see Leinster’s <a href='http://arxiv.org/abs/math.CT/0305049'>book</a>, 10.2).</p> </li> <li> <p>A. Joyal, <em>Remarques sur la théorie des jeux à deux personnes</em>, Gazette des Sciences Mathematiques du Québec 1(4):46–52, 1977; Robin Houston’s rough translation <a href='https://bosker.wordpress.com/2009/11/16/the-category-of-conway-games/'>can be found here</a></p> </li> <li> <p>André Joyal, <em>Free lattices, communication and money games</em>, in: Logic and scientific methods. Volume one of the proceedings of the tenth international congress of logic, methodology and philosophy of science, Florence, Italy, Synth. Libr. 259, pages 29–68. Dordrecht: Kluwer Academic Publishers, 1997.</p> </li> </ul> <p><div class='property'> category: <a class='category_link' href='/nlab/list/people'>people</a></div></p> <p> </p> </div> <div class="revisedby"> <p> Last revised on September 1, 2024 at 08:08:00. 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