homomorphism

Etymology

homo- + morphism.

noun

1. (algebra) A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.
   A field homomorphism is a map from one field to another one which is additive, multiplicative, zero-preserving, and unit-preserving.
   1954, Kuo-Tsai Chen, Iterated Integrals and Exponential Homomorphisms, Proceedings of the London Mathematical Society, Reprinted in 2001, Philippe Tondeur (editor), Collected Papers of K.-T. Chen, Birkhäuser, page 54, This motivates a generalization, and exponential homomorphisms are now defined, in an algebraic fashion, from certain free products to formal power series rings with non-commutative indeterminates.
   A homomorphism of presheaves h:A→B is a collection of homomorphisms h_U:A(U)→B(U) commuting with restrictions. 1997, Glen E. Bredon, Sheaf Theory, 2nd edition, Springer, page 8
   Definition 1.15. Let G and H be matrix Lie groups. A map Φ from G to H is called a Lie group homomorphism if (1) Φ is a group homomorphism and (2) Φ is continuous. 2003, Brian C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Springer, page 17
2. (biology) A similar appearance of two unrelated organisms or structures.