A Criterion for Kan Extensions of Lax Monoidal Functors
Category Theory
2018-09-28 v1
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 Melli\`es-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.
Keywords
Cite
@article{arxiv.1809.10481,
title = {A Criterion for Kan Extensions of Lax Monoidal Functors},
author = {Tobias Fritz and Paolo Perrone},
journal= {arXiv preprint arXiv:1809.10481},
year = {2018}
}
Comments
20 pages, partial overlap with Appendix B of arXiv:1712.05363, not intended for publication