The category of strictly unital A∞-categories with strict morphisms admits a cofibrantly generated model structure with quasi-equivalences as weak equivalences.
A remark on fibrancy of ($\mbox{A$_{\infty}$Cat}$,$W^{\tiny\mbox{A}_{\infty}}_{\tiny\mbox{qe}}$)
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this note we prove the existence, in the category of (strictly unital) A$_{\infty}$categories, of the pullback of a (strictly unital) A$_{\infty}$functor, satisfying a particular property (denoted by F1), along any A$_{\infty}$functor. As a consequence we provide a positive answer to Pascaleff's question whether (A$_{\infty}$Cat,$W^{\tiny\mbox{A}_{\infty}}_{\tiny\mbox{qe}}$) is a fibrant object in RelCat.
citation-role summary
background 1
citation-polarity summary
fields
math.CT 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
A model structure on the category of A$_\infty$-categories with strict morphisms
The category of strictly unital A∞-categories with strict morphisms admits a cofibrantly generated model structure with quasi-equivalences as weak equivalences.