Coinverters and categories of fractions for categories with structure
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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.
Mathematics Subject Classifications (1991)18D99 18A30 18A35
Key wordsCategory of fractions coinverter reflexive coinverter categories with structure
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- 1.Jean Benabou: 1989, ‘Some remarks on 2-categorical algebra’,Bulletin de la Société Mathématique de Belgique 41, 127–194.Google Scholar
- 2.R. Blackwell, G.M. Kelly, and J. Power: 1989, ‘Two-dimensional monad theory’,J. Pure Appl. Algebra 59, 1–41.Google Scholar
- 3.Brian Day: 1973, ‘Note on monoidal localisation’,Bull. Austral. Math. Soc. 8, 1–16.Google Scholar
- 4.P. Gabriel and M. Zisman: 1967,Calculus of Fractions and Homotopy Theory, Springer-Verlag, Berlin.Google Scholar
- 5.P.T. Johnstone: 1977,Topos Theory, Academic Press, London.Google Scholar
- 6.G.M. Kelly: 1989, ‘Elementary observations on 2-categorical limits’,Bull. Austral. Math. Soc. 39, 301–317.Google Scholar
- 7.G.M. Kelly and Stephen Lack: 1993, ‘Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads’,Applied Categorical Structures 1, 85–94 (this issue).Google Scholar