i am wanting to know what a terminal (final) object in the coslice category
might be (technically, where "A" is the functor:
and where the other functor of the comma category is
alternatively, if it is easier to explain this as an intial object in the slice category:
, that's fine as well.
so the initial object in the slice category is the unique map from the initial object of Set (ok, technically the initial object and the map, but i'm trying to "forget about objects")?
if that is so, then the final object in the coslice category should be...(*,{*}) where {*} is a "generic" singleton set, and * is the only possible arrow (constant map), yes?
what is motivating these questions is that i know that for a given function f:A-->Z, the projection p:A-->A/~f is initial in the coslice category (A ↓ Set),
and i am wondering about the possible "dual statements".