Christopher Townsend writes:

Is anyone aware of an explicit description of the coinvertor of a diagram -> [R^op,Set] -> [C^op,Set]

in CoComp (the two arrows are f,g, and there is a natural transofrmation, \alpha:f->g, to be coinverted). C,R are small categories, and the category CoComp is the category of (small) cocomplete categories.

Thank you, Christopher Townsend (Open University)

The functors f and g are cocontinuous functors between presheaf categories, so have right adjoints f* and g*. The natural transformation alpha:f->g induces a natural transformation alpha*:g*->f*. The coinverter in CoComp of alpha is the inverter in Comp of alpha*, but the latter can actually be formed in Cat. It is the full subcategory of [C^op,Set] consisting of all objects X for which alpha*X:g*X->f*X is invertible. Steve Lack. 27-Nov-2002 12:21:48 -0400,2447;000000000000-00000000