Abstract
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 operationsA n →A forn εN along with natural transformations and equations, passes canonically to the categoryA [Σ−1] of fractions, provided that Σ 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.
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The first and third authors gratefully acknowledge the support of the Australian Research Council.
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Kelly, G.M., Lack, S. & Walters, R.F.C. Coinverters and categories of fractions for categories with structure. Appl Categor Struct 1, 95–102 (1993). https://doi.org/10.1007/BF00872988
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DOI: https://doi.org/10.1007/BF00872988