* horizontal composition in a 2-category
@ 2010-10-04 12:42 David Leduc
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From: David Leduc @ 2010-10-04 12:42 UTC (permalink / raw)
To: categories
Hi,
A 2-category C is a category enriched over Cat. This gives me two compositions.
* The functor C(Y,Z) x C(X,Y) -> C(X,Z)
* and for each X and Y in C the function (C(X,Y))(g,h) x
(C(X,Y))(f,g) -> (C(X,Y))(f,h)
But how can I derive the horizontal composition:
(C(Y,Z))(g1,g2) x (C(X,Y))(f1,f2) -> (C(X,Z))(g1 o f1, g2 o f2) = ???
I the case of the 2-category of categories, I know how to define
horizontal composition (Godement product) in a pointwise manner, but
how does it generalize to 2-categories?
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