Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.braid_natural

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

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

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproducts