isomorphism

plural isomorphisms

1. countableuncountableSimilarity 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

   1. countableuncountablebiologythe 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.
   2. countableuncountablechemistrythe 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

   3. countableuncountablehuman sciencesthe similarity in the structure or processes of different organizations.
2. A one-to-one correspondence
   1. countableuncountablegroup algebraA bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings.
   2. countableuncountablecomputera one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets.
   3. countableuncountablecategory theoryA 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