Coalgebraic structure from weak limit preserving functors
H. Peter Gumm, Tobias Schröder · Electronic Notes in Theoretical Computer Science · 2000
Given an endofunctor F on the category of sets, we investigate how the structure theory of SetF, 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 SetF in terms of congruences and bisimulations, which explains, under which conditions monos must be injective maps.