Theorems · Definition · category theory

CategoryTheory.constantSheafAdj

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      (D : Type u_2) →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
          [inst_2 : CategoryTheory.HasWeakSheafify J D] →
            {T : C} →
              CategoryTheory.Limits.IsTerminal T →
                (CategoryTheory.constantSheaf J D ⊣ (CategoryTheory.sheafSections J D).obj (Opposite.op T))

The constant sheaf functor is left adjoint to evaluation at a terminal object.

Defined in

Mathlib.CategoryTheory.Sites.ConstantSheaf

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify