For the term in sociology, see isomorphism (sociology).

In mathematics, an isomorphism (Greek:isos "equal", and morphe "shape") is a bijective map f such that both f and its inverse f ⁻¹ are homomorphisms, i.e. structure-preserving mappings.

Informally, an isomorphism is a kind of mapping between objects, which shows a relationship between two properties or operations. If there exists an isomorphism between two structures, we call the two structures isomorphic. In a certain sense, Isomorphic sets are structurally identical, if you choose to ignore finer-grained differences that may arise from how they are defined.

According to Douglas Hofstadter:

"The word "isomorphism" applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where "corresponding" means that the two parts play similar roles in their respective structures." (Gödel, Escher, Bach, p. 49)

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StackExchange: Infinity de Rham quasi-isomorphism - http://stackexchangesites.com/lXX
stackexchange (stackexchange) Thu, 31 Dec 2009 20:55:01 -0000
StackExchange: Infinity de Rham quasi-isomorphism - http://stackexchangesites.com/lXX
Methodist #.adeptness ails undistinguished #.able isomorphism #.interpret blackout
supertitleduccu (Supertitled Uccu) Mon, 28 Dec 2009 11:57:35 -0000
Methodist #.adeptness ails undistinguished #.able isomorphism #.interpret blackout
isomorphism.
Wildknees (Danny Barnes) Sun, 27 Dec 2009 15:19:10 -0000
isomorphism.
yazim: Isomorphism of Destiny. http://bit.ly/6TxJuD
theluckdoctor (Michael Searles) Thu, 24 Dec 2009 18:18:29 -0000
yazim: Isomorphism of Destiny. http://bit.ly/6TxJuD

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