isomorphism

A morphism

f : A \to B

is an isomorphism if it has an inverse, i.e. a morphism

f^{-1} : B \to A

satisfying

f \circ f^{-1} = \id_B

and

f^{-1} \circ f = \id_A

Dual isomorphism (self-dual) Related epimorphism, monomorphism, split epimorphism, split monomorphism External nLab link

Relevant implications

epimorphism andextremal monomorphism implies isomorphism
epimorphism andmonomorphism implies isomorphism
epimorphism andsplit monomorphism implies isomorphism
epimorphism implies isomorphism
extremal epimorphism andmonomorphism implies isomorphism
isomorphism implies effective epimorphism andsplit epimorphism
isomorphism implies effective monomorphism andsplit monomorphism
isomorphism implies normal epimorphism
isomorphism implies normal monomorphism
monomorphism andsplit epimorphism implies isomorphism
monomorphism implies isomorphism

Examples

There are 2 morphisms with this property.

Counterexamples

There are 13 morphisms without this property.

Unknown

There are 0 morphisms for which the database has no information on whether they satisfy this property.

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