april aka cyberglot on Nostr: I’m reading “Formal metatheory of second-order abstract syntax” by Fiore and ...

I’m reading “Formal metatheory of second-order abstract syntax” by Fiore and Szamozvancev. On pages 6-7, they introduce a skew-monoidal closed structure, and then they say this (pic 1). I was interested on why a dependent sum is skewed, so I found out it’s a left adjoint to the base change functor (pic 2). Now, what coends have to do with the base change functor? Or they don’t have anything to do with each other, it’s just that dependent sums are left-leaning and don’t preserve colimits?