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arXiv · 1409.6405

Kan extensions and cartesian monoidal categories

Ross Street
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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.

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Ross Street. 2014-09-23. Kan extensions and cartesian monoidal categories. https://arxiv.org/abs/1409.6405

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