I'm trying to prove that hom-sets in an abelian category have a canonical abelian group structure, working with this definition of an abelian category:
A category is abelian if
- It has a zero object
- It has all finite (co)products
- Every morphism has a (co)kernel
- Every monomorphism is a kernel and every epimorphism is a cokernel
My approach is to first construct pullbacks, and I think I can do this once I have equalizers, but I'm having trouble constructing those. Any help is appreciated!