Theorems · Definition · category theory

CategoryTheory.Limits.isColimitMapCoconeEmptyCoconeEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          (X : C) →
            CategoryTheory.Limits.IsColimit (G.mapCocone (CategoryTheory.Limits.asEmptyCocone X)) ≃
              CategoryTheory.Limits.IsInitial (G.obj X)

The map of an empty cocone is a colimit iff the mapped object is initial.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal

Cited by

1 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category