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Unitalities and mapping spaces in $A_\infty$-categories

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arxiv 2407.05532 v1 pith:JIKNRGDW submitted 2024-07-08 math.CT math.SG

Hiro Lee Tanaka This is my paper · ORCID
classification math.CTmath.SG
keywords unitala-infinity-categoriesfunctorsinfinity-categorymappingspacesstrictlya-infinity--categories
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We prove, over any base ring, that the infinity-category of strictly unital A-infinity-categories (and strictly unital functors) is equivalent to the infinity-category of unital A-infinity-categories (and unital functors). We also identify various models for internal homs and mapping spaces in the infinity-categories of dg-categories and of A-infinity--categories, generalizing results of To\"en and Faonte.

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  1. A model structure on the category of A$_\infty$-categories with strict morphisms

    math.CT 2025-06 conditional novelty 6.0 of 10

    The category of strictly unital A∞-categories with strict morphisms admits a cofibrantly generated model structure with quasi-equivalences as weak equivalences.

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