Coinverters and categories of fractions for categories with structure

G.M. Kelly, Stephen Lack, and R.F.C. Walters

This appeared in Applied Categorical Structures 1:95-102, 1993.

A category of fractions is a special case of a coinverter in the 2-category Cat. We observe that, in a cartesian closed 2-category, the product of two reflexive coinverter diagrams is another such diagram. It follows that an equational structure on a category A, if given by operations from An to A (for natural numbers n) along with natural transformations and equations, passes canonically to the category A[S-1] of fractions, provided that S is closed under the operations. We exhibit categories with such structures as algebras for a class of 2-monads on Cat, to be called strongly finitary monads.


Steve Lack
Last modified: Tue Sep 12 17:03:25 EST 2000