Isomorphism

//ˌaɪsə(ʊ)ˈmɔɹfɪzəm// noun

noun ·Uncommon ·Advanced level

Definitions

Noun
  1. 1
    Similarity of form countable, uncountable

    "The postulated isomorphism between words and things constitutes the characterizing feature of all philosophically based universal languages."

  2. 2
    (biology) similarity or identity of form or shape or structure wordnet
  3. 3
    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. countable, uncountable
  4. 4
    Similarity of form; the similarity in the crystal structures of similar chemical compounds. countable, uncountable

    "The isomorphism of compounds does not prove the isomorphism of their respective constituents."

  5. 5
    Similarity of form; the similarity in the structure or processes of different organizations. countable, uncountable
Show 3 more definitions
  1. 6
    A one-to-one correspondence; A bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings. countable, uncountable
  2. 7
    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. countable, uncountable
  3. 8
    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). countable, uncountable

Synonyms

All synonyms
isoisomorphy

Example

More examples

"The module has only countably many direct summands up to isomorphism."

Etymology

From iso- + -morphism.

Related phrases

Curry-Howard isomorphismfirst isomorphism theoremnatural isomorphismquasi-isomorphismring isomorphism

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.