Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} {A : Type u'}
  [inst_1 : CategoryTheory.Category.{v', u'} A] [inst_2 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A]
  {Φ₁ Φ₂ Φ₃ : J.Point} (f : Φ₁ ⟶ Φ₂) (g : Φ₂ ⟶ Φ₃) {Z : CategoryTheory.Functor (CategoryTheory.Functor Cᵒᵖ A) A}
  (h : Φ₁.presheafFiber ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber (CategoryTheory.CategoryStruct.comp f g)) h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber g)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber f) h)

Defined in

Mathlib.CategoryTheory.Sites.Point.Category

Cited by

0 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize