isomorphism

1. (countable, uncountable)Similarity of form

   (biology) similarity or identity of form or shape or structure

2. Similarity of form

   (countable, uncountable)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.

   изоморфи́змizomorfízm

   ізоморфі́змizomorfízm

3. (countable, uncountable)The similarity in the crystal structures of similar chemical compounds.

4. (countable, uncountable)The similarity in the structure or processes of different organizations.

5. A one-to-one correspondence

   (countable, uncountable)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 between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets.

7. (countable, uncountable)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).

1. Few languages have audio-visual isomorphism.

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

   deDer Modul hat bis auf Isomorphie nur abzählbar viele direkte Summanden.

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3. The diagram above commutes if and only if f is an isomorphism.

   deDas obige Diagramm kommutiert genau dann, wenn f ein Isomorphismus ist.

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regular