Abstract

Given an endofunctor F on the category of sets, we investigate how the structure theory of Set F , the category of F -coalgebras, depends on certain preservation properties of F . In particular, we consider preservation of various weak limits and obtain corresponding conditions on bisimulations and subcoalgebras. We give a characterization of monos in Set F in terms of congruences and bisimulations, which explains, under which conditions monos must be injective maps.

Citations