Theorems · Theorem · category theory

CategoryTheory.Limits.PreservesColimitPair.of_iso_coprod_comparison

∀ {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 Y : C) [inst_2 : CategoryTheory.Limits.HasBinaryCoproduct X Y]
  [inst_3 : CategoryTheory.Limits.HasBinaryCoproduct (G.obj X) (G.obj Y)]
  [i : CategoryTheory.IsIso (CategoryTheory.Limits.coprodComparison G X Y)],
  CategoryTheory.Limits.PreservesColimit (CategoryTheory.Limits.pair X Y) G

If the coproduct comparison map for G at (X,Y) is an isomorphism, then G preserves the pair of (X,Y).

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasBinaryCoproductCategoryTheory.Limits.HasBinaryCoproductCategoryTheory.IsIso