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Stream: theory: category theory

Topic: Does this functor have a right adjoint?

Chad Nester (Nov 25 2020 at 14:36):

I wonder if anyone can help me with this:

Let $\mathsf{Prod}$ be the category of categories with finite products and product preserving functors, and let $\mathsf{Lex}$ be the category of categories with finite limits and finite limit preserving functors. There is a forgetful functor $U : \mathsf{Lex} \to \mathsf{Prod}$. This $U$ has a left adjoint, given by the finite limit completion of a category with finite products. Does $U$ have a right adjoint?