Simplification for Graph-like Objects.

This paper unifies different notions of simplification for graphs into a single universal construction on a comma category, given the familiar conditions of faithfulness, regularity, and existence of an adjoint. Specifically, this construction unifies the passage of a directed multigraph to a simple digraph, the passage of a set-system hypergraph to a simple set system, and the passage of an incidence hypergraph to a simple incidence structure. Moreover, this universal construction has a natural dual, a "cosimplification". This dual process unifies the removal of isolated vertices and loose edges for quivers and incidence hypergraphs, as well as the passage of a set-system hypergraph to a set system when using antihomomorphisms.