In the CwF instance for a presheaf category, contexts are in Psh(C), and types over Γ are in Psh(el(Γ)). You define context extension as (Γ.A)(k) := Σ(g :Γ(k)).A(k,g) in Psh(C)
Question: is there a way to define this more abstractly? Like with the dependent sum or something?
Basically, I'm trying to convince Lean that (Γ.A) is actually a presheaf, and the dependent equalities are kicking my butt, despite the proof being trivial on paper.
But if there's a way to express this using known operations that are guaranteed to produce presheaves as output, then this might be easier
