Theorems · Theorem · category theory

CategoryTheory.Limits.prod.lift_map_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {V W X Y Z : C}
  [inst_1 : CategoryTheory.Limits.HasBinaryProduct W X] [inst_2 : CategoryTheory.Limits.HasBinaryProduct Y Z]
  (f : V ⟶ W) (g : V ⟶ X) (h : W ⟶ Y) (k : X ⟶ Z) {Z_1 : C} (h_1 : Y ⨯ Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prod.lift f g)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prod.map h k) h_1) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.prod.lift (CategoryTheory.CategoryStruct.comp f h)
        (CategoryTheory.CategoryStruct.comp g k))
      h_1

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

8 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasBinaryProduct