A Criterion for Kan Extensions of Lax Monoidal Functors

Tobias Fritz and Paolo Perrone

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Submission date: 27. Sep. 2018
Pages: 22
Bibtex
MSC-Numbers: 18A30, 18C10, 18D10
Keywords and phrases: Kan extensions, monoidal categories, Monads
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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 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.