Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.IsLocalSite.faithful_constantSheaf

∀ {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).Faithful

Defined in

Mathlib.CategoryTheory.Sites.LocalSite

Cited by

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Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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