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Is there a construction capturing indexed families of adjunctions?

I'm sorry in advance if this question does not belong on this site. I am curious as to what is "really" going on when you have a family of functors indexed by elements in a base category, all of which ...
Mathemologist's user avatar
1 vote
0 answers
118 views

Existence and explicit descriptions for left and right Kan extensions and lifts in bicategories of spans

Given a category $\mathcal{C}$, it follows from Proposition 4.1 of Day's Brian Day, Limit spaces and closed span categories, Lecture Notes in Mathematics, 420, 1974 (doi:10.1007/BFb0063100). That ...
crystalline cohomology's user avatar
1 vote
0 answers
60 views

Second order lambda calculus as dinatural transformations in some category of CCCs

Let $\textbf{CART}$ be a category where the objects are all Cartesian closed categories (henceforth shortened as CCC). Is there any way to define the arrows so that $\textbf{CART}$ itself becomes ...
Johan Thiborg-Ericson's user avatar