Diagram chasing in ordered categories with involution

AbstractTo carry out diagram chases in non-additive categories, we make use of categories of relations, ordered categories with involution. For illustration, we give two constructions of the connecting homomorphism. In the top-down treatment, morphisms are just relations with right adjoints. In the bottom–up treatment for a category with a given class of regular epimorphisms, we construct relations following a method of Calenko