# Are homomorphisms antisymmetric? [duplicate]

I was wondering whether the antisymmetry of cardinality (expressed in the Shroeder-Bernstein Theorem) carries over to homomorphisms. That is, if A and B are algebraic structures of the same type, and there is an injective homomorphism from A to B, and there is an injective homomorphism from B to A, then are A and B necessarily isomorphic?