Theorems · Theorem · category theory

CategoryTheory.Limits.prodComparison_natural_of_natTrans

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{w, u₂} D]
  {F : CategoryTheory.Functor C D} {A B : C} [inst_2 : CategoryTheory.Limits.HasBinaryProduct A B]
  [inst_3 : CategoryTheory.Limits.HasBinaryProduct (F.obj A) (F.obj B)] {H : CategoryTheory.Functor C D}
  [inst_4 : CategoryTheory.Limits.HasBinaryProduct (H.obj A) (H.obj B)] (α : F ⟶ H),
  CategoryTheory.CategoryStruct.comp (α.app (A ⨯ B)) (CategoryTheory.Limits.prodComparison H A B) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prodComparison F A B)
      (CategoryTheory.Limits.prod.map (α.app A) (α.app B))

Naturality of the prodComparison morphism in a natural transformation.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

1 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasBinaryProduct