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

Xiaofa Chen; Mattia Ornaghi

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

Category Theory 2024-12-19 v1

Authors: Xiaofa Chen , Mattia Ornaghi

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.

Keywords

A-infinity category fibrant object pullback relative category A-infinity functor model structure

Cite

@article{arxiv.2412.13347,
  title  = {A remark on fibrancy of ($\mbox{A$_{\infty}$Cat}$,$W^{\tiny\mbox{A}_{\infty}}_{\tiny\mbox{qe}}$)},
  author = {Xiaofa Chen and Mattia Ornaghi},
  journal= {arXiv preprint arXiv:2412.13347},
  year   = {2024}
}

Comments

12 pages. Comments are welcome

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

Abstract

Keywords

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