Spahn couniversal mapping property 1 (changes)

Showing changes from revision #4 to #5: Added | Removed | Changed

Let F:XCF:X\to C be a functor between categories. A CC morphism f:aF(x)f:a\to F(x) is called to satisfy the couniversal mapping property with respect to FF or we say that ff is a couniversal arrow from cc to FF or that ff is the initial arrow from cc to FF, if f=0C/Ff=0\in C/F is initial in the comma category c/Fc/F.

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

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

commutes.

Last revised on July 23, 2012 at 18:09:49. See the history of this page for a list of all contributions to it.