Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
83/2018

A Criterion for Kan Extensions of Lax Monoidal Functors

Tobias Fritz and Paolo Perrone

Abstract

In this mainly expository note, we state a criterion for when a left Kan extension of a lax monoidal functor along a strong monoidal functor can itself be equipped with a lax monoidal structure, in a way that results in a left Kan extension in MonCat. This belongs to the general theory of algebraic Kan extensions, as developed by Melliès-Tabareau, Koudenburg and Weber, and is very close to an instance of a theorem of Koudenburg. We find this special case particularly important due to its connections with the theory of graded monads.

Received:
Sep 27, 2018
Published:
Oct 16, 2018
MSC Codes:
18A30, 18C10, 18D10
Keywords:
Kan extensions, monoidal categories, Monads

Related publications

Preprint
2018 Repository Open Access
Tobias Fritz and Paolo Perrone

A criterion for Kan extensions of lax monoidal functors