Theorems · Definition · category theory

CategoryTheory.sheafifyLift

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      {D : Type u_1} →
        [inst_1 : CategoryTheory.Category.{v_1, u_1} D] →
          [inst_2 : CategoryTheory.HasWeakSheafify J D] →
            {P Q : CategoryTheory.Functor Cᵒᵖ D} →
              (P ⟶ Q) → CategoryTheory.Presheaf.IsSheaf J Q → (CategoryTheory.sheafify J P ⟶ Q)

Given a sheaf Q and a morphism P ⟶ Q, construct a morphism from sheafify J P to Q.

Defined in

Mathlib.CategoryTheory.Sites.Sheafification

Cited by

18 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify