Dictionary

isomorphism en · NOUN

Pronunciation

• /ˌaɪsə(ʊ)ˈmɔɹfɪzəm/
• (US) audio

Etymology

From iso- + -morphism.

Meanings

1. (countable, uncountable) Similarity of form
   • The postulated isomorphism between words and things constitutes the characterizing feature of all philosophically based universal languages. 1984, Brigitte Asbach-Schnitker, “Introduction”, in Mercury or The Secret and Swift Messenger, →ISBN:
2. (countable, uncountable) Similarity of form ▸ the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology.
3. (countable, uncountable) Similarity of form ▸ the similarity in the crystal structures of similar chemical compounds.
   • The isomorphism of compounds does not prove the isomorphism of their respective constituents. 1874, C. Rammelsberg, “Crystallographic and chemical relations of the natural sulphides, arsenides, and sulpharsenides”, in The Chemical News and Journal of Physical Science, page 197:
4. (countable, uncountable) Similarity of form ▸ the similarity in the structure or processes of different organizations.
5. (countable, qualifier:group algebra, uncountable) A one-to-one correspondence ▸ A bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings.
6. (countable, uncountable) A one-to-one correspondence ▸ a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets.
7. (countable, uncountable) A one-to-one correspondence ▸ A morphism which has a two-sided inverse; the composition of the morphism and such an inverse yields either one of two identity morphisms (depending on the order of composition).

Forms

Antonyms

anisomorphism

Deriveds

ring isomorphism · symplectomorphism · quasi-isomorphism · Curry-Howard isomorphism · first isomorphism theorem · natural isomorphism

Relateds

Isomorphism on Wolfram MathWorld · isomorphous · Graph Isomorphism on Wolfram MathWorld · Isomorphism on Encyclopedia of Mathematics · Natural Isomorphism on Wolfram MathWorld · isomorphism on nLab · isomorphic

Synonyms

iso (in category theory)

Translations (31)

hi तुल्याकारिता (bidirectionally structure-preserving bijection) · pt isomorfismo (the similarity in form of organisms of different ancestry) · sh izomorfizam (the similarity in form of organisms of different ancestry) · nl isomorfisme (bidirectionally structure-preserving bijection) · cs izomorfismus (the similarity in form of organisms of different ancestry) · fi isomorfismi (the similarity in form of organisms of different ancestry) · cs izomorfismus (bidirectionally structure-preserving bijection) · uk ізоморфі́зм (the similarity in form of organisms of different ancestry) · tl kasanyuan (the similarity in form of organisms of different ancestry) · bg изоморфизъм (bidirectionally structure-preserving bijection) · it isomorfismo (the similarity in form of organisms of different ancestry) · is einsmótun (bidirectionally structure-preserving bijection) · fr isomorphisme (the similarity in form of organisms of different ancestry) · cmn 同構 /同构 (bidirectionally structure-preserving bijection) · ru изоморфизм (bidirectionally structure-preserving bijection) · hu izomorfizmus (the similarity in form of organisms of different ancestry) · fr isomorphisme (bidirectionally structure-preserving bijection) · hu izomorfia (bidirectionally structure-preserving bijection) · eo izomorfio (bidirectionally structure-preserving bijection) · kk изоморфизм (bidirectionally structure-preserving bijection) · ru изоморфи́зм (the similarity in form of organisms of different ancestry) · bg изоморфи́зъм (the similarity in form of organisms of different ancestry) · hi समाकृतिकता (bidirectionally structure-preserving bijection) · pl izomorfizm (the similarity in form of organisms of different ancestry) · es isomorfismo (bidirectionally structure-preserving bijection) · da isomorfi (bidirectionally structure-preserving bijection) · es isomorfismo (the similarity in form of organisms of different ancestry) · de Isomorphismus (bidirectionally structure-preserving bijection) · pl izomorfizm (bidirectionally structure-preserving bijection) · pt isomorfismo (bidirectionally structure-preserving bijection) · fi isomorfismi (bidirectionally structure-preserving bijection)