In my last post, I proved a neat little theorem in category theory: that if \(C\) and \(D\) are categories with pushouts, then the category \(C \to D\) of pushout-preserving functors from \(C\) to \(D\) itself has pushouts. Here, I'm going to develop a construct similar to pushouts, but a little more general. Generalized pushouts A pushout is a construction you might be able to perform in a category on two arrows \(f\) and \(g\) that have a common source. If \(f : A \to B\) and \(g : A \to C\...
