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

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