The Kleisli Category is a Category Of Fractions

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.