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A remark on fibrancy of ($\mbox{A$_{\infty}$Cat}$,$W^{\tiny\mbox{A}_{\infty}}_{\tiny\mbox{qe}}$)
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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.
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Cited by 1 Pith paper
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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.
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