homomorphism

== English == === Etymology === From homo- +‎ morphism. === Pronunciation === === Noun === homomorphism (plural homomorphisms) (algebra) A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces. Coordinate term: homology 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. (biology) A similar appearance of two unrelated organisms or structures, as for example with fish and whales. Coordinate term: homology ==== Usage notes ==== In mathematics, this word is largely interchangeable with morphism. However, one uses morphism almost exclusively in the context of category theory, while homomorphism is more common in algebra. ==== Hyponyms ==== (structure-preserving map between algebraic structures): automorphism, endomorphism, epimorphism, isomorphism, linear map, monomorphism ==== Derived terms ==== ==== Related terms ==== morphism ==== Translations ==== ==== See also ==== (biology): convergent evolution === Further reading === Group homomorphism on Wikipedia.Wikipedia Ring homomorphism on Wikipedia.Wikipedia Linear map on Wikipedia.Wikipedia Algebra homomorphism on Wikipedia.Wikipedia Glossary of field theory on Wikipedia.Wikipedia Semigroup on Wikipedia.Wikipedia Homomorphism on Encyclopedia of Mathematics homomorphism on nLab