  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.
