Theorems · Theorem · category theory

CategoryTheory.Sheaf.isConstant_iff_mem_essImage

∀ {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]
  {L : CategoryTheory.Functor D (CategoryTheory.Sheaf J D)} {T : C} (hT : CategoryTheory.Limits.IsTerminal T)
  (adj : L ⊣ (CategoryTheory.sheafSections J D).obj (Opposite.op T)) (F : CategoryTheory.Sheaf J D),
  CategoryTheory.Sheaf.IsConstant J F ↔ L.essImage F

Defined in

Mathlib.CategoryTheory.Sites.ConstantSheaf

Cited by

5 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify