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arXiv · 2202.06805

On presheaf submonads of quantale enriched categories

Maria Manuel Clementino·Carlos Fitas
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Abstract

This paper focus on the presheaf monad and its submonads on the realm of $V$-categories, for a quantale $V$. First we present two characterisations of presheaf submonads, both using $V$-distributors: one based on admissible classes of $V$-distributors, and other using Beck-Chevalley conditions on $V$-distributors. Then we focus on the study of the corresponding Eilenberg-Moore categories of algebras, having as main examples the formal ball monad and the so-called Lawvere monad.

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Maria Manuel Clementino, Carlos Fitas. 2022-02-14. On presheaf submonads of quantale enriched categories. https://arxiv.org/abs/2202.06805

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