Scholarlink

<p>We provide details of the proof of Lurie’s theorem on operadic Kan extensions. Along the way, we generalize the construction of monoidal envelopes of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10485_2025_9821_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\infty \)</EquationSource> </InlineEquation>-operads to families of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10485_2025_9821_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\infty \)</EquationSource> </InlineEquation>-operads and use it to construct the fiberwise direct sum functor, both of which we characterize by certain universal properties. Aside from their use in elaborating the proof of Lurie’s theorem, these results and constructions have their independent interest.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Monoidal Envelopes of Families of \(\infty \)-Operads and \(\infty \)-Operadic Kan Extensions

  • 期刊论文

  • 发表日期：

    2025年7月18日

查看全文
  • Kensuke Arakawa

摘要

We provide details of the proof of Lurie’s theorem on operadic Kan extensions. Along the way, we generalize the construction of monoidal envelopes of \(\infty \) -operads to families of \(\infty \) -operads and use it to construct the fiberwise direct sum functor, both of which we characterize by certain universal properties. Aside from their use in elaborating the proof of Lurie’s theorem, these results and constructions have their independent interest.