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V-localizations andV-Kleisli algebras

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Abstract

We prove a pushout theorem for localizations and Kleisli categories over a symmetric monoidal closed categoryV. That is, suppose ∑ is aV-localizable subcategory of aV-categoryA and thatT=(T,η,μ) is aV-monad onA. Then under suitable relations betweenT and ∑ we show that there is aV-monadT′ induced onA[∑-1] such that the Kleisli category ofT′ is the pushout of the localization functor Φ:A→A[∑-1] and the free functor F:A→K(T). Consequently,K(T′)≈K(T) [S-1] for some S ⊑K(T). We give several examples of this situation.

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  1. Department of Mathematics, The University of Texas, 78712, Austin, Texas, USA

    Harvey Wolff

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  1. Harvey Wolff
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Wolff, H. V-localizations andV-Kleisli algebras. Manuscripta Math 16, 203–228 (1975). https://doi.org/10.1007/BF01164425

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