Re: Name for a concept

Jean Benabou wrote:

(2)- In most cases the canonical map being epic is not what one really wants. Of course Joyal assumes the category where the maps live to be a pre-topos, then it's enough, otherwise one cannot "compose" such squares. Do we have to rename the squares where the canonical map is a universal epi, or those where its a universal regular epi?

very good point i suggest, since we can live with epics, strict(=regular) epis, universal such, etc etc, we should have: quasi-pullback strict(=regular) quasi pullback universal quasi-pullback of course, the useful concept being: "strict universal quasi-pullback" e.d.