An example of the non-existence of coequalizers in the category of the A${}_{\infty }$-categories

Abstract

We prove that the categories of strictly unital (resp.\ non unital) A${}_{\infty }$-algebras and A${}_{\infty }$-categories, with strictly unital (resp.\ non unital) A${}_{\infty }$-morphisms and A${}_{\infty }$-functors have no coequalizers.

arXiv comment6 pages. Comments are very welcome