Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.IsLocalSite.fullyFaithfulConstantSheaf

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      [CategoryTheory.LocallySmall.{w, v, u} C] →
        [J.IsLocalSite] →
          (A : Type u') →
            [inst_3 : CategoryTheory.Category.{v', u'} A] →
              [CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A] →
                [CategoryTheory.Limits.HasProducts A] →
                  [inst_6 : CategoryTheory.HasWeakSheafify J A] → (CategoryTheory.constantSheaf J A).FullyFaithful

On local sites, the constant sheaf functor is fully faithful.

Defined in

Mathlib.CategoryTheory.Sites.LocalSite

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.GrothendieckTopology.IsLocalSiteCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSizeCategoryTheory.Limits.HasProductsCategoryTheory.HasWeakSheafify