Deformations of quasi-categories in modules

Arne Mertens; Violeta Borges Marques; Wendy Lowen

Deformations of quasi-categories in modules

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arxiv 2308.09148 v1 pith:7JR5LG3Z submitted 2023-08-17 math.CT math.ATmath.KT

Violeta Borges Marques , Wendy Lowen , Arne Mertens This is my paper · ORCID

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The framework of templicial objects was put forth in arXiv:2302.02484v1 in order to develop higher categorical concepts in the presence of enrichment. In particular, quasi-categories in modules constitute a subclass of templicial modules which may be considered as a kind of "weak dg-categories (concentrated in homologically positive degrees)" according to arXiv:2005.04778v3. The main goal of the present paper is to initiate the deformation theory of templicial modules. In particular, we show that quasi-categories in modules are preserved under levelwise flat infinitesimal deformation.

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Templicial nerve of an A-infinity category
math.CT 2024-11 conditional novelty 6.0 of 10

The authors define a templicial A-infinity nerve functor that lifts Faonte's simplicial A-infinity nerve to vector-space-enriched templicial objects and prove it is a quasi-category in vector spaces.

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