Pushout Invariance Revisited

Abstract

Abstract With modest standing assumptions on a category C, it is shown that a Galois connection exists between subclasses of C-objects (on the one hand) and classes of epimorphisms of C (on the other). In this connection the following classes are in a one-to-one correspondence, which reverses inclusion: the epireflective classes of C-objects with the classes ε of epimorphisms which are pushout invariant, in the sense that, for each pushout diagram in which e ∈ ε, then it follows that n ∈ ε. The paper then examines some of the consequences of this result, and in so doing “revisits” the pushout invariance of the authors as it was discussed in a paper of some fifteen years ago.