Connectedness classes

Abstract

Let X be an (E,M)-category for sinks. A recently introduced notion of connectedness with respect to a closure operator C on X and to a class of X-monomorphisms N is further analyzed. The notion of N-connectedness hull of a class of X-objects is introduced and a characterization of it is presented under the assumption of N being closed under the formation of pullbacks. Moreover, a characterization of the related notion of N-connectedness class is presented under the assumption that X contains a terminal object. Some examples are provided.

Quaestiones Mathematicae 23(2000), 313–334