Difference between revisions of "Bimorphism"
From Encyclopedia of Mathematics
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''bijective morphism in a category'' | ''bijective morphism in a category'' | ||
| − | One of the categoric-theoretical generalizations of the concept of a bijective mapping between sets. A morphism | + | One of the categoric-theoretical generalizations of the concept of a bijective mapping between sets. A morphism $u$ in a category $C$ is said to be a bimorphism if it is both a [[Monomorphism|monomorphism]] and an [[Epimorphism|epimorphism]] in $C$. A product of bimorphisms is a bimorphism, i.e. the bimorphisms form a subcategory containing all isomorphisms. In the category of sets and the category of groups every bimorphism is an isomorphism. However, the categories of rings, topological spaces, or Abelian groups without torsion contain bimorphisms that are not isomorphisms. |
Latest revision as of 11:34, 29 June 2014
bijective morphism in a category
One of the categoric-theoretical generalizations of the concept of a bijective mapping between sets. A morphism $u$ in a category $C$ is said to be a bimorphism if it is both a monomorphism and an epimorphism in $C$. A product of bimorphisms is a bimorphism, i.e. the bimorphisms form a subcategory containing all isomorphisms. In the category of sets and the category of groups every bimorphism is an isomorphism. However, the categories of rings, topological spaces, or Abelian groups without torsion contain bimorphisms that are not isomorphisms.
How to Cite This Entry:
Bimorphism. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bimorphism&oldid=14918
Bimorphism. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bimorphism&oldid=14918
This article was adapted from an original article by I.V. DolgachevM.Sh. Tsalenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article