A Criterion for Kan Extensions of Lax Monoidal Functors

Tobias Fritz; Paolo Perrone

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arXiv · 1809.10481

A Criterion for Kan Extensions of Lax Monoidal Functors

Tobias Fritz·Paolo Perrone

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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.

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Tobias Fritz, Paolo Perrone. 2018-09-27. A Criterion for Kan Extensions of Lax Monoidal Functors. https://arxiv.org/abs/1809.10481

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