Isomorphism (category theory)
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Revision as of 14:19, 13 March 2016 by Alec (Talk | contribs) (Alec moved page Isomorphism to Isomorphism (category theory) without leaving a redirect: There are loads of different isomorphisms, while this superceeds all, they're still needed)
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Contents
Definition
Given a pair of arrows, [ilmath]A\mathop{\longrightarrow}^fB[/ilmath] and [ilmath]B\mathop{\longrightarrow}^g A[/ilmath] in a category [ilmath]\mathscr{C} [/ilmath], we say that [ilmath]f[/ilmath] and [ilmath]g[/ilmath] are isomorphisms[1] if:
- [ilmath]g\circ f=\text{Id}_A[/ilmath] and [ilmath]f\circ g=\text{Id}_B[/ilmath]
We may also call [ilmath]f[/ilmath] and [ilmath]g[/ilmath] an inverse pair of isomorphisms. For clarity I say again: both [ilmath]f[/ilmath] and [ilmath]g[/ilmath] are themselves isomorphisms
See also
References
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