Bartosz Milewski on Nostr: For me the connection between categorical limits and calculus appears when you can ...

For me the connection between categorical limits and calculus appears when you can define an iterative process, expecially if a category is a poset or is filtered.

For instance, you get a fixed point of an algebra by iterating the powers of a functor. Or you are defining smaller and smaller neighborhoods using sieves or sigma-algebras (hence integrals).

I realize this is handwaving, but categorical nomenclature evolved by generalizing concrete concepts from other areas of math.