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Please update your browser bookmarks and please use the default browser print function instead.</div></div><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="English">English</h2></div> <div class="interproject-box sister-wikipedia sister-project noprint floatright"><div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/44px-Wikipedia-logo-v2.svg.png" decoding="async" width="44" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/66px-Wikipedia-logo-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/88px-Wikipedia-logo-v2.svg.png 2x" data-file-width="103" data-file-height="94" /></span><figcaption></figcaption></figure></div><div style="margin-left: 60px;">English <a href="/wiki/Wikipedia" title="Wikipedia">Wikipedia</a> has an article on:<div style="margin-left: 10px;"><b class="Latn" lang="en"><a href="https://en.wikipedia.org/wiki/category_theory" class="extiw" title="w:category theory">category theory</a></b></div></div><span class="interProject"><a href="https://en.wikipedia.org/wiki/category_theory" class="extiw" title="w:category theory">Wikipedia </a></span></div><style data-mw-deduplicate="TemplateStyles:r81571951">.mw-parser-output .interproject-box{font-size:90%;width:250px;padding:4px;text-align:left;background:var(--wikt-palette-paleblue,#f9f9f9);border:var(--border-color-base,#aaa)1px solid}@media screen and (max-width:719px){.mw-parser-output .interproject-box{box-sizing:border-box;line-height:1.5;width:100%;max-width:100%}}</style> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r81571951"><div class="sister-wikipedia sister-project noprint"><div class="floatright interproject-box"> <div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><a href="/wiki/File:Wikibooks-logo-en.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Wikibooks-logo-en.svg/50px-Wikibooks-logo-en.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Wikibooks-logo-en.svg/75px-Wikibooks-logo-en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Wikibooks-logo-en.svg/100px-Wikibooks-logo-en.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption></figcaption></figure></div> <div style="margin-left: 60px;">Wikibooks has more about this subject: <div style="margin-left: 10px;"><i><b><a href="https://en.wikibooks.org/wiki/Haskell/Category_theory" class="extiw" title="wikibooks:Haskell/Category theory">Haskell/Category theory</a></b></i></div> </div> </div></div><p><span class="interProject"><a href="https://en.wikibooks.org/wiki/Haskell/Category_theory" class="extiw" title="wikibooks:Haskell/Category theory">Wikibooks <sup></sup></a></span> </p><div class="mw-heading mw-heading3"><h3 id="Noun">Noun</h3></div> <p><span class="headword-line"><strong class="Latn headword" lang="en"><a href="/wiki/category#English" title="category">category</a> <a href="/wiki/theory#English" title="theory">theory</a></strong> (<i><a href="/wiki/Appendix:Glossary#uncountable" title="Appendix:Glossary">uncountable</a></i>)</span> </p> <ol><li><span class="usage-label-sense"><span class="ib-brac label-brac">(</span><span class="ib-content label-content"><a href="/wiki/mathematics" title="mathematics">mathematics</a></span><span class="ib-brac label-brac">)</span></span> A branch of <a href="/wiki/mathematics" title="mathematics">mathematics</a> which deals with spaces and maps between them in <a href="/wiki/abstraction" title="abstraction">abstraction</a>, taking similar <a href="/wiki/theorems" title="theorems">theorems</a> from various disparate more concrete branches of mathematics and unifying them. <ul><li><div class="citation-whole"><span class="cited-source"><span class="None" lang="und"><b>1984</b></span>, Robert Goldblatt, <cite><a rel="nofollow" class="external text" href="http://ebooks.library.cornell.edu/cgi/t/text/pageviewer-idx?c=math;cc=math;idno=gold010;view=image;seq=19;size=100;page=root">Topoi, the categorial analysis of logic</a></cite>, page 3:</span><dl><dd><div class="h-quotation"><span class="Latn e-quotation cited-passage" lang="en">As mentioned earlier set theory provides a general conceptual framework for mathematics. Now, since <strong class="selflink">category theory</strong>, through the notion of topos, has succeeded in axiomatising set-theory, the outcome is an entirely new <i>categorial foundation of mathematics</i>! The category-theorists attitude that "function" rather than "set membership" can be seen as the fundamental mathematical concept has been entirely vindicated. The pre-eminent role of set theory in contemporary mathematics is suddenly challenged. A revolution has occurred in the history of mathematical ideas (albeit a peaceful one) that will undoubtedly influence the direction of the path to the future.</span></div></dd></dl></div></li></ul></li></ol> <div class="mw-heading mw-heading4"><h4 id="Hypernyms">Hypernyms</h4></div> <ul><li><span class="Latn" lang="en"><a href="/wiki/mathematics#English" title="mathematics">mathematics</a></span>, <span class="Latn" lang="en"><a href="/wiki/theory#English" title="theory">theory</a></span></li></ul> <div class="mw-heading mw-heading4"><h4 id="Translations">Translations</h4></div> <div class="NavFrame" id="Translations-branch_of_mathematics"><div class="NavHead" style="text-align:left">branch of mathematics</div><div class="NavContent"><table class="translations" role="presentation" data-gloss="branch of mathematics"><tbody><tr><td class="translations-cell multicolumn-list" colspan="3"><style data-mw-deduplicate="TemplateStyles:r81584270">.mw-parser-output .translations{width:100%}.mw-parser-output .translations-cell{background-color:var(--wikt-palette-lightyellow,#FFFFe0);vertical-align:top;text-align:left}</style> <ul><li>Chinese: <dl><dd>Mandarin: <span class="Hant" lang="cmn"><a href="/wiki/%E7%AF%84%E7%96%87%E8%AB%96#Mandarin" title="範疇論">範疇論</a></span><span class="Zsym mention" style="font-size:100%;"> / </span><span class="Hans" lang="cmn"><a href="/wiki/%E8%8C%83%E7%95%B4%E8%AE%BA#Mandarin" title="范畴论">范畴论</a></span><span class="tpos"> <a href="https://zh.wiktionary.org/wiki/%E7%AF%84%E7%96%87%E8%AB%96" class="extiw" title="zh:範疇論">(zh)</a></span> <span class="mention-gloss-paren annotation-paren">(</span><span lang="cmn-Latn" class="tr Latn">fànchóulùn</span><span class="mention-gloss-paren annotation-paren">)</span></dd></dl></li> <li>Czech: <span class="Latn" lang="cs"><a href="/wiki/teorie_kategori%C3%AD#Czech" title="teorie kategorií">teorie kategorií</a></span> <span class="gender"><abbr title="feminine gender">f</abbr></span></li> <li>Finnish: <span class="Latn" lang="fi"><a href="/wiki/kategoriateoria#Finnish" title="kategoriateoria">kategoriateoria</a></span></li> <li>French: <span class="Latn" lang="fr"><a href="/w/index.php?title=th%C3%A9orie_des_cat%C3%A9gories&action=edit&redlink=1" class="new" title="théorie des catégories (page does not exist)">théorie des catégories</a></span><span class="tpos"> <a href="https://fr.wiktionary.org/wiki/th%C3%A9orie_des_cat%C3%A9gories" class="extiw" title="fr:théorie des catégories">(fr)</a></span> <span class="gender"><abbr title="feminine gender">f</abbr></span></li> <li>German: <span class="Latn" lang="de"><a href="/wiki/Kategorientheorie#German" title="Kategorientheorie">Kategorientheorie</a></span> <span class="gender"><abbr title="feminine gender">f</abbr></span></li> <li>Icelandic: <span class="Latn" lang="is"><a href="/wiki/r%C3%ADkjafr%C3%A6%C3%B0i#Icelandic" title="ríkjafræði">ríkjafræði</a></span> <span class="gender"><abbr title="feminine gender">f</abbr></span></li> <li>Japanese: <span class="Jpan" lang="ja"><a href="/wiki/%E5%9C%8F%E8%AB%96#Japanese" title="圏論">圏論</a></span> <span class="mention-gloss-paren annotation-paren">(</span><span class="tr">けんろん, kenron</span><span class="mention-gloss-paren annotation-paren">)</span></li> <li>Korean: <span class="Kore" lang="ko"><a href="/wiki/%EB%B2%94%EC%A3%BC%EB%A1%A0#Korean" title="범주론">범주론(範疇論)</a></span> <span class="mention-gloss-paren annotation-paren">(</span><span lang="ko-Latn" class="tr Latn">beomjuron</span><span class="mention-gloss-paren annotation-paren">)</span></li> <li>Malay: <span class="Latn" lang="ms"><a href="/w/index.php?title=teori_kategori&action=edit&redlink=1" class="new" title="teori kategori (page does not exist)">teori kategori</a></span></li> <li>Romanian: <span class="Latn" lang="ro"><a href="/w/index.php?title=teoria_categoriei&action=edit&redlink=1" class="new" title="teoria categoriei (page does not exist)">teoria categoriei</a></span> <span class="gender"><abbr title="feminine gender">f</abbr></span></li> <li>Russian: <span class="Cyrl" lang="ru"><a href="/w/index.php?title=%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BA%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D0%B9&action=edit&redlink=1" class="new" title="теория категорий (page does not exist)">теория категорий</a></span> <span class="gender"><abbr title="feminine gender">f</abbr></span> <span class="mention-gloss-paren annotation-paren">(</span><span lang="ru-Latn" class="tr Latn">teorija kategorij</span><span class="mention-gloss-paren annotation-paren">)</span></li> <li>Spanish: <span class="Latn" lang="es"><a href="/wiki/teor%C3%ADa_de_categor%C3%ADas#Spanish" title="teoría de categorías">teoría de categorías</a></span> <span class="gender"><abbr title="feminine gender">f</abbr></span></li> <li>Swedish: <span class="Latn" lang="sv"><a href="/wiki/kategoriteori#Swedish" title="kategoriteori">kategoriteori</a></span><span class="tpos"> <a href="https://sv.wiktionary.org/wiki/kategoriteori" class="extiw" title="sv:kategoriteori">(sv)</a></span> <span class="gender"><abbr title="common gender">c</abbr></span></li> <li>Turkish: <span class="Latn" lang="tr"><a href="/wiki/kategori_teorisi#Turkish" title="kategori teorisi">kategori teorisi</a></span>, <span class="Latn" lang="tr"><a href="/wiki/ulam_kuram%C4%B1#Turkish" title="ulam kuramı">ulam kuramı</a></span></li></ul> </td></tr></tbody></table></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wiktionary.org/w/index.php?title=category_theory&oldid=83139010">https://en.wiktionary.org/w/index.php?title=category_theory&oldid=83139010</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div 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