CatGloss

(Compare Exercise X.) Let A \mathscr{A} be a category and AA A \in \mathscr{A} . Define a quotient object of A A to be an isomorphism class of epics out of A A . That is, let Epic(A) \mathbf{Epic}(A) be the full subcategory of A/A A/\mathscr{A} whose objects are the epics; then a quotient object of A A is an isomorphism class of objects of Epic(A) \mathbf{Epic}(A) .