A category is abelian if\n1. it has a zero object $0$, that is both initial and terminal,\n2. it has all binary products and binary coproducts,\n3. it has all kernels and cokernels, defined respectively to be the equalizer and coequalizer of a map $f \colon A \to B$ with the zero map $A \to 0 \to B$, and\n4. all monomorphisms and epimorphisms arise as kernels or cokernels, respectively.