isomorphism
noun/ˌaɪsə(ʊ)ˈmɔɹfɪzəm/
Etymology From iso- + -morphism.
7 senses
- 1Similarity of form
- 2the similarity in form of organisms, which may be due to…
- 3the similarity in the crystal structures of similar…
- 4the similarity in the structure or processes of…
- 5A bijection f such that both f and its inverse f⁻¹ are…
- 6a one-to-one correspondence between all the elements of…
- 7A morphism which has a two-sided inverse; the…
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:
Biology, Natural sciences 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.
Chemistry, Natural sciences, Physical sciences 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:
Human sciences, Sciences, Social science, Sociology the similarity in the structure or processes of different organizations.
› A one-to-one correspondence
A bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings.
Computer, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Science, Sciences 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.
Category theory, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences 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).
- Synonyms
- iso
- Antonyms
- anisomorphism
- Derived terms
- Curry-Howard isomorphism, first isomorphism theorem, natural isomorphism, quasi-isomorphism, ring isomorphism, symplectomorphism
- Related terms
- isomorphic, isomorphous, Isomorphism on Encyclopedia of Mathematics, isomorphism on nLab, Isomorphism on Wolfram MathWorld, Graph Isomorphism on Wolfram MathWorld, Natural Isomorphism on Wolfram MathWorld