Coinverters and categories of fractions for categories with structure

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)95-102
Number of pages8
JournalApplied Categorical Structures
Issue number1
Publication statusPublished - Mar 1993
Externally publishedYes


  • categories with structure
  • Category of fractions
  • coinverter
  • Mathematics Subject Classifications (1991): 18D99, 18A30, 18A35
  • reflexive coinverter


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