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A morphism
in a category is an isomorphism if there exists a morphism
which is its inverse. The objects and are isomorphic if there is an isomorphism between them.
A morphism which is both an isomorphism and an endomorphism is called an automorphism. The set of automorphisms of an object is denoted
.
Examples:
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"isomorphism" is owned by djao.
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(view preamble)
| Also defines: |
isomorphic, automorphism |
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Cross-references: homeomorphism, continuous maps, topological spaces, invertible linear transformation, linear transformations, vector spaces, map, ring homomorphisms, rings, group homomorphisms, groups, bijective, functions, category of sets, objects, inverse, category, morphism
There are 223 references to this entry.
This is version 3 of isomorphism, born on 2002-02-13, modified 2005-11-30.
Object id is 1936, canonical name is Isomorphism2.
Accessed 26504 times total.
Classification:
| AMS MSC: | 18A05 (Category theory; homological algebra :: General theory of categories and functors :: Definitions, generalizations) | | | 20A05 (Group theory and generalizations :: Foundations :: Axiomatics and elementary properties) | | | 13A99 (Commutative rings and algebras :: General commutative ring theory :: Miscellaneous) | | | 15A04 (Linear and multilinear algebra; matrix theory :: Linear transformations, semilinear transformations) | | | 54A05 (General topology :: Generalities :: Topological spaces and generalizations ) |
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Pending Errata and Addenda
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