The Kleisli Category is a Category Of Fractions

Author: Giuli E.   Hardie K.A.   Vermeulen J.J.C.  

Publisher: Taylor & Francis Ltd

ISSN: 1607-3606

Source: Quaestiones Mathematicae, Vol.25, Iss.3, 2002-09, pp. : 397-403

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Abstract

We consider a generalised notion of category of fractions associated with a class Φ of permitted replacement situations between zig-zags in a category C. The Kleisli category associated with a monad [T, η, μ] in C is shown to be a special case in which the arrows {ηX X ∈ C} become left-invertible after passage to fractions.