A remark on fibrancy of ($\mbox{A$_{\infty}$Cat}$,$W^{\tiny\mbox{A}_{\infty}}_{\tiny\mbox{qe}}$)

Xiaofa Chen; Mattia Ornaghi

paper

A remark on fibrancy of ($\mbox{A$_{\infty}$Cat}$,$W^{\tiny\mbox{A}_{\infty}}_{\tiny\mbox{qe}}$)

arXiv:2412.13347

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.

12 pages. Comments are welcome