Theorems · Theorem · category theory

CategoryTheory.Meq.congr_apply

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} {D : Type w}
  [inst_1 : CategoryTheory.Category.{w', w} D] {FD : D → D → Type u_1} {CD : D → Type t}
  [inst_2 : (X Y : D) → FunLike (FD X Y) (CD X) (CD Y)] [inst_3 : CategoryTheory.ConcreteCategory D FD] {X : C}
  {P : CategoryTheory.Functor Cᵒᵖ D} {S : J.Cover X} (x : CategoryTheory.Meq P S) {Y : C} {f g : Y ⟶ X} (h : f = g)
  (hf : (↑S).arrows f), ↑x { Y := Y, f := f, hf := hf } = ↑x { Y := Y, f := g, hf := ⋯ }

Defined in

Mathlib.CategoryTheory.Sites.ConcreteSheafification

Cited by

1 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory