2014/09/23 by Street, Ross · 1 citation
#18A40 #18C10 #18D10 #18D20 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1409.6405
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.