Applied Categorical Structures

, Volume 1, Issue 1, pp 95–102 | Cite as

Coinverters and categories of fractions for categories with structure

  • G. M. Kelly
  • Stephen Lack
  • R. F. C. Walters


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−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.

Mathematics Subject Classifications (1991)

18D99 18A30 18A35 

Key words

Category of fractions coinverter reflexive coinverter categories with structure 


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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • G. M. Kelly
    • 1
  • Stephen Lack
    • 1
  • R. F. C. Walters
    • 1
  1. 1.School of Mathematics and Statistics F07University of SyndyeAustralia

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