Theorems · Theorem · category theory

CategoryTheory.Sum.natTransOfWhiskerLeftInlInr_comp

∀ {A : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} A] {A' : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} A'] {B : Type u} [inst_2 : CategoryTheory.Category.{v, u} B]
  {F G H : CategoryTheory.Functor (A ⊕ A') B}
  (η₁ : (CategoryTheory.Sum.inl_ A A').comp F ⟶ (CategoryTheory.Sum.inl_ A A').comp G)
  (η₂ : (CategoryTheory.Sum.inr_ A A').comp F ⟶ (CategoryTheory.Sum.inr_ A A').comp G)
  (ν₁ : (CategoryTheory.Sum.inl_ A A').comp G ⟶ (CategoryTheory.Sum.inl_ A A').comp H)
  (ν₂ : (CategoryTheory.Sum.inr_ A A').comp G ⟶ (CategoryTheory.Sum.inr_ A A').comp H),
  CategoryTheory.Sum.natTransOfWhiskerLeftInlInr (CategoryTheory.CategoryStruct.comp η₁ ν₁)
      (CategoryTheory.CategoryStruct.comp η₂ ν₂) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Sum.natTransOfWhiskerLeftInlInr η₁ η₂)
      (CategoryTheory.Sum.natTransOfWhiskerLeftInlInr ν₁ ν₂)

Defined in

Mathlib.CategoryTheory.Sums.Products

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category