Coinverters and categories of fractions for categories with structure

A category of fractions is a special case of acoinverter in the 2-categoryCat. We observe that, in a cartesian closed 2-category, the product of tworeflexive coinverter diagrams is another such diagram. It follows that an equational structure on a categoryA, if given by operationsAⁿ A forn N along with natural transformations and equations, passes canonically to the categoryA [^–1] of fractions, provided that is closed under the operations. We exhibit categories with such structures as algebras for a class of 2-monads onCat, to be calledstrongly finitary monads.The first and third authors gratefully acknowledge the support of the Australian Research Council.