Categories of fractions and infinitary structures

Steve Lack (14/08/96)

This talk was a gentle introduction to categories of fractions and coinverters, and conditions under which structure on a category passes to the category of fractions. Most of the talk was taken up in a summary of left and right caculi of fractions (Gabriel-Zisman), pullback congruences (Bénabou) and the theorem of Kelly-Lack-Walters that for T a strongly-finitary 2-monad on Cat, the forgetful 2-functor from T-Alg to Cat creates reflexive coinverters.

It was then noted that this can be extended to 2-monads involving operations of possibly infinite but still discrete arity, at the expense of making the assumption that the class $\Sigma$ of arrows to be inverted admit a calculus of left or right fractions.

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Steve Lack

Last modified: Tue May 19 10:44:26 EST 1998