A Model Structure on the Category of $\text{ A}_{\infty }$-Categories with Strict Morphisms

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2026年5月4日

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Mattia Ornaghi

摘要

We prove that the category of (strictly unital) $\text{ A}_{\infty }$ $A_{\infty}$ -categories, linear over a commutative ring R, with strict $\text{ A}_{\infty }$ $A_{\infty}$ -morphisms has a cofibrantly generated model structure. In this model structure every object is fibrant and the cofibrant objects have cofibrant morphisms. As a consequence we prove that the semi-free $\text{ A}_{\infty }$ $A_{\infty}$ -categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure.

A Model Structure on the Category of \(\text{ A}_{\infty }\)-Categories with Strict Morphisms

摘要