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 An →A for n εN along with natural transformations and equations, passes canonically to the category A [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 on Cat, to be called strongly finitary monads.
- categories with structure
- Category of fractions
- Mathematics Subject Classifications (1991): 18D99, 18A30, 18A35
- reflexive coinverter