different between isomorphism vs diffeomorphism

English

iso- +? -morphism

isomorphism (plural isomorphisms)

Similarity of form
- 1984 Brigitte Asbach-Schnitker, "Introduction", Mercury or The Secret and Swift Messenger, ?ISBN.
  The postulated isomorphism between words and things constitutes the characterizing feature of all philosophically based universal languages.
1. (biology) 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.
2. (chemistry) the similarity in the crystal structures of similar chemical compounds
  - 1874 C. Rammelsberg, "Crystallographic and chemical relations of the natural sulphides, arsenides, and sulpharsenides", The Chemical News and Journal of Physical Science, page 197.
    The isomorphism of compounds does not prove the isomorphism of their respective constituents.
3. (sociology) the similarity in the structure or processes of different organizations
A one-to-one correspondence
1. (group algebra) A bijection f such that both f and its inverse f^?1 are homomorphisms, that is, structure-preserving mappings.
2. (computer science) 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
3. (category theory) A morphism which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).

diffeomorphism (plural diffeomorphisms)

(mathematics) A differentiable homeomorphism (with differentiable inverse) between differentiable manifolds.

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