What question did this study set out to answer?

To establish a model structure on strictly unital A∞-categories with strict A∞-morphisms.

May 6, 2026Open Access

A Model Structure on the Category of A -Categories with Strict Morphisms

Key Points

To establish a model structure on strictly unital A∞-categories with strict A∞-morphisms.
Prove that the category has a cofibrantly generated model structure.
Demonstrate that every object is fibrant and cofibrant objects have cofibrant morphisms.
Semi-free A∞-categories are confirmed as cofibrant objects in the model structure.
Resolution categories are shown to be cofibrant as well.

Abstract

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

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Cite This Study

Mattia Ornaghi (Mon,) studied this question.

synapsesocial.com/papers/69faa28f04f884e66b53320c https://doi.org/https://doi.org/10.1007/s10485-026-09870-2