Mike Stay wrote:
Is there a more common term for a "graph shift"?
I don't know - I'm curious. But the term "transformation" would be logical. We all know about natural transformations, but we can also drop the naturality condition: given functors F, F': C -> C', a "transformation" from F to F' assigns to each object c in C a morphism from F(c) to F(c'). Since a category is a graph with extra structure, but the concept of "transformation" doesn't invoke this extra structure, we can also speak of a transformation between homomorphisms between graphs - which is just what you're calling a "graph shift". Then there's a forgetful 2-functor from [categories, functors, natural transformations] to [graphs, graph homomorphisms, transformations] But if there's already a standard term, I recommend that you use that! Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]