  Abelian categories provide a self-dual axiomatic context for establishing
homomorphism theorems (such as the isomorphism theorems and homological diagram
lemmas) for abelian groups, and more generally, modules. In this paper we
describe a self-dual context which allows one to establish the same theorems in
the case of non-abelian group-like structures; the question of whether such a
context can be found has been left open for seventy years. We also formulate
and prove in our context a universal isomorphism theorem from which all other
isomorphism theorems can be deduced.
