Original Articles

The Kleisli Category is a Category Of Fractions

Published in: Quaestiones Mathematicae
Volume 25 , issue 3 , 2002 , pages: 397–403

DOI: 10.2989/16073600209486025

Author(s): E. Giuli , K.A. Hardie , J.J.C. Vermeulen

Keywords: KLEISLI CATEGORY , MONAD , 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.

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