1. Let C be a category, with domain function dom, codomain function cod, and composition law o. Define a new category Cp, its opposite category, to have the same objects and morphisms, but with domain function dom p cod, codomain function codP = dom, and composition law o defined by fog = go f. (a) Verify that COP is in fact a category with Homcor (A, B) = Home(B,A). (b) Show that initial objects in C are final objects in Cp and that final objects in C are initial objects in Cp. (c) Show that the epimorphisms in C are the monomorphisms in COP and that the monomorphisms in COP are the epimorphisms in C. 1. Let C be a category, with domain function dom, codomain function cod, and composition law o. Define a new category Cp, its opposite category, to have the same objects and morphisms, but with domain function dom p cod, codomain function codP = dom, and composition law o defined by fog = go f. (a) Verify that COP is in fact a category with Homcor (A, B) = Home(B,A). (b) Show that initial objects in C are final objects in Cp and that final objects in C are initial objects in Cp. (c) Show that the epimorphisms in C are the monomorphisms in COP and that the monomorphisms in COP are the epimorphisms in C