In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures (such as groups, rings, or vector spaces). The word homomorphism comes from the ancient Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "shape". Isomorphisms, automorphisms, and endomorphisms are all types of homomorphism.
Read more about Homomorphism: Informal Discussion, Relation To Category Theory, Kernel of A Homomorphism, Homomorphisms of Relational Structures, Homomorphisms and E-free Homomorphisms in Formal Language Theory