CategoryTheory.Over.pullback.proof_1

theorem CategoryTheory.Over.pullback.proof_1 : ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C] {X Y : C} (f : X ⟶ Y) (g : CategoryTheory.Over Y), CategoryTheory.Limits.HasLimit (CategoryTheory.Limits.cospan g.hom f)

The theorem `CategoryTheory.Over.pullback.proof_1` states that for any category `C` that has pullbacks, given objects `X` and `Y` in `C`, a morphism `f` from `X` to `Y`, and a "over" object `g` over `Y`, there exists a limit for the cospan formed by the homomorphism of `g` and `f`. In the context of category theory, a cospan is a diagram indexed by the shape of a walking cospan, and "having a limit" essentially means that there exists a certain universal object with respect to this diagram.

More concisely: Given a category with pullbacks, for any object X, Y, and morphisms f : X -> Y and g : Z -> Y, the cospan (g, f) has a limit.