It is shown that any inverse semigroup of endomorphisms of an object in aproperly (E,M)-structured category admitting pullbacks may be embedded in the inverse monoid of partial automorphisms between retracts of that object. It follows that every inverse monoid is isomorphic with the inverse monoid of all partial automorphisms between [non-trivial] retracts of some object A of any [almost] algebraically universal and properly (E,M)-structured category with pullbacks, in particular, of an [almost] algebraically universal and finitely complete category with arbitrary intersections. Several examples are given.