Kan extensions and cartesian monoidal categories
Category Theory
2014-09-24 v1
Abstract
The existence of adjoints to algebraic functors between categories of models of Lawvere theories follows from finite-product-preservingness surviving left Kan extension. A result along these lines was proved in Appendix 2 of Brian Day's 1970 PhD thesis. His context was categories enriched in a cartesian closed base. A generalization is described here with essentially the same proof. We introduce the notion of cartesian monoidal category in the enriched context. With an advanced viewpoint, we give a result about left extension along a promonoidal module and further related results.
Cite
@article{arxiv.1409.6405,
title = {Kan extensions and cartesian monoidal categories},
author = {Ross Street},
journal= {arXiv preprint arXiv:1409.6405},
year = {2014}
}