The Partial Simplicial Category and Algebras for Monads

TL;DR

This paper explicitly constructs weights on the simplicial category to facilitate the formation of Kleisli and Eilenberg-Moore objects in 2-categories, advancing the understanding of monad-related structures.

Contribution

It introduces explicit weights on the simplicial category that enable the construction of Kleisli and Eilenberg-Moore objects via colimits and limits in 2-categories.

Findings

Explicit weights on the simplicial category are constructed.

Colimits and limits with these weights yield Kleisli and Eilenberg-Moore objects.

Enhances the categorical framework for monads in 2-categories.

Abstract

We construct explicitly the weights on the simplicial category so that the colimits and limits of 2-functors with those weights provide the Kleisli objects and the Eilenberg-Moore objects, respectively, in any 2-category.