Theorems · Definition · category theory

CategoryTheory.Meq.pullback

{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] →
                  {Y X : C} →
                    {P : CategoryTheory.Functor Cᵒᵖ D} →
                      {S : J.Cover X} →
                        CategoryTheory.Meq P S → (f : Y ⟶ X) → CategoryTheory.Meq P ((J.pullback f).obj S)

Pull back a term of Meq P S with respect to a morphism f : Y ⟶ X in C.

Defined in

Mathlib.CategoryTheory.Sites.ConcreteSheafification

Cited by

5 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory