Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.diagramNatTrans_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type w}
  [inst_1 : CategoryTheory.Category.{w', w} D]
  [inst_2 :
    ∀ (P : CategoryTheory.Functor Cᵒᵖ D) (X : C) (S : J.Cover X), CategoryTheory.Limits.HasMultiequalizer (S.index P)]
  {P Q R : CategoryTheory.Functor Cᵒᵖ D} (η : P ⟶ Q) (γ : Q ⟶ R) (X : C),
  J.diagramNatTrans (CategoryTheory.CategoryStruct.comp η γ) X =
    CategoryTheory.CategoryStruct.comp (J.diagramNatTrans η X) (J.diagramNatTrans γ X)

Defined in

Mathlib.CategoryTheory.Sites.Plus

Cited by

1 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasMultiequalizer