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

Mattia Ornaghi

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arXiv · 2506.22847

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

Mattia Ornaghi

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Abstract

We prove that the category of (strictly unital) A$_\infty$-categories, linear over a commutative ring $R$, with strict 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 A$_\infty$-categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure.

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Mattia Ornaghi. 2025-06-28. A model structure on the category of A$_\infty$-categories with strict morphisms. https://arxiv.org/abs/2506.22847

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