Adjoint functor theorems for ∞ ∞∞ ‐categories

机译：伴随汇流器定理 ∞ ∞∞ - 类别

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Abstract > Adjoint functor theorems give necessary and sufficient conditions for a functor to admit an adjoint. In this paper, we prove general adjoint functor theorems for functors between <mat:math display="inline" altimg="urn:x-wiley:00246107:media:jlms12282:jlms12282-math-0003" wiley:location="equation/jlms12282-math-0003.png"> <mat:mi>∞</mat:mi> </mat:math> ‐categories. One of our main results is an <mat:math display="inline" altimg="urn:x-wiley:00246107:media:jlms12282:jlms12282-math-0004" wiley:location="equation/jlms12282-math-0004.png"> <mat:mi>∞</mat:mi> </mat:math> ‐categorical generalization of Freyd's classical General Adjoint Functor Theorem. As an application of this result, we recover Lurie's adjoint functor theorems for presentable <mat:math display="inline" altimg="urn:x-wiley:00246107:media:jlms12282:jlms12282-math-0005" wiley:location="equation/jlms12282-math-0005.png"> <mat:mi>∞</mat:mi> </mat:math> ‐categories. We also discuss the comparison between adjunctions of <mat:math display="inline" altimg="urn:x-wiley:00246107:media:jlms12282:jlms12282-math-0006" wiley:location="equation/jlms12282-math-0006.png"> <mat:mi>∞</mat:mi> </mat:math> ‐categories and homotopy adjunctions, and give a treatment of Brown representability for <mat:math display="inline" altimg="urn:x-wiley:00246107:media:jlms12282:jlms12282-math-0007" wiley:location="equation/jlms12282-math-0007.png"> <mat:mi>∞</mat:mi> </mat:math> ‐categories based on Heller's purely categorical formulation of the classical Brown representability?theorem. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> > 伴随函授理定理为娱乐提供了必要和充分的条件，以承认伴随。在本文中，我们证明了归档的汇流归乐器定理 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：JLMS12282：JLMS12282-Math-0003”Wiley：Location =“等式/ JLMS12282-Math-0003.png”> <mat：mi>∞</ mat：mi> </ mat：math> - 类别。我们的主要结果之一是 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：JLMS12282：JLMS12282-Math-0004”Wiley：Location =“等式/ JLMS12282-Math-0004.png”> <mat：mi>∞</ mat：mi> </ mat：math> - Freyd古典普通伴奏算法定理的分类概括。作为此结果的应用，我们恢复LURIE的伴随算子定理 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：JLMS12282：JLMS12282-Math-0005”Wiley：Location =“等式/ JLMS12282-Math-0005.png”> <mat：mi>∞</ mat：mi> </ mat：math> - 类别。我们还讨论了对应之间的比较 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：jlms12282：jlms12282-math-0006”Wiley：location =“等式/ jlms12282-math-0006.png”> <mat：mi>∞</ mat：mi> </ mat：math> - 类别和同型作用，并造成棕色可爱的处理 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：JLMS12282：JLMS12282-Math-0007”Wiley：location =“等式/ jlms12282-math-0007.png”> <mat：mi>∞</ mat：mi> </ mat：math> - 基于Heller纯粹的分类制定的古典棕色可爱的类别？定理。 </ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-31023/'>《The Journal of the London Mathematical Society》</a> <b style="margin: 0 2px;">|</b><span>2020年第2期</span><b style="margin: 0 2px;">|</b><span>共23页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Nguyen Hoang Kim&option=202" target="_blank" rel="nofollow">Nguyen Hoang Kim;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Raptis George&option=202" target="_blank" rel="nofollow">Raptis George;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Schrade Christoph&option=202" target="_blank" rel="nofollow">Schrade Christoph;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Fakult?t für MathematikUniversit?t RegensburgD‐93040 Regensburg Germany;</p> <p>Fakult?t für MathematikUniversit?t RegensburgD‐93040 Regensburg Germany;</p> <p>Mathematisches InstitutWWU MünsterD‐48149 Münster Germany;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/156.html" title="数学">数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=18A40&option=203" rel="nofollow">18A40;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=55U35&option=203" rel="nofollow">55U35;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=55U40 (primary)&option=203" rel="nofollow">55U40 (primary);</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=18G55 (secondary)&option=203" rel="nofollow">18G55 (secondary);</a> </p> <div class="translation"> 机译：18A40;55U35;55U40（初级）;18G55（二次）; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div 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