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

IF 0.5 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2025-07-18 DOI:10.1007/s10485-025-09821-3

Kensuke Arakawa

引用次数: 0

Abstract

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.

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\(\infty \) -操作数和\(\infty \) -操作数Kan扩展族的一元包络

给出了Lurie定理在可操作Kan扩展上的证明。在此过程中，我们将\(\infty \) -操作元的一元包络的构造推广到\(\infty \) -操作元族，并用它来构造纤维直和函子，并用某些全称性质对这两个函子进行了刻画。这些结果和构造除了用于阐述Lurie定理的证明之外，还有其独立的意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.