2018/09/27 by Fritz, Tobias, Perrone, Paolo
#18A30 #18C10 #18D10 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1809.10481
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.