Spahn couniversal mapping property 1 (Rev #2, changes)

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LetF:XCF:X\to C be a functor between categories. An A object x CX x\in C X is morphism called to satisfy auniversal mapping property with respect to FF and a morphism f:aF(x)f:a\to F(x)f:aF(x)f:a\to F(x) if is for called any to satisfy theyXy\in Xcouniversal mapping property with respect to FF, if f=0C/Ff=0\in C/F is initial in the comma category C/FC/F. and any morphism ϕ:aG(y)\phi:a\to G(y) there is a morphism ψ:xy\psi:x\to y such that

a f F(x) ϕ G(ψ) G(y)\array{ a&\stackrel{f}{\mapsto}&F(x) \\ &\searrow^\phi&\downarrow^{G(\psi)} \\ &&G(y) }

This means: for any yXy\in X and any morphism ϕ:aG(y)\phi:a\to G(y) there is a morphism ψ:xy\psi:x\to y such that

a f F(x) ϕ G(ψ) G(y)\array{ a&\stackrel{f}{\mapsto}&F(x) \\ &\searrow^\phi&\downarrow^{G(\psi)} \\ &&G(y) }

commutes.

Revision on July 14, 2012 at 22:45:15 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.