homomorphism

1. (algebra) A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.Examples: "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#58;A#92;rightarrowB is a collection of homomorphisms h#95;U#58;A(U)#92;rightarrowB(U) commuting with restrictions."

2. (biology) A similar appearance of two unrelated organisms or structures, as for example with fish and whales.