Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.associator_natural_assoc

∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {U V W X Y Z : C} (f : U ⟶ X) (g : V ⟶ Y) (h : W ⟶ Z) {Z_1 : C}
  (h_1 : X ⊞ Y ⊞ Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.map (CategoryTheory.Limits.biprod.map f g) h)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.associator X Y Z).hom h_1) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.associator U V W).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.map f (CategoryTheory.Limits.biprod.map g h))
        h_1)

The associator isomorphism can be passed through a map by swapping the order.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproducts