Theorems · Theorem · category theory

CategoryTheory.Equivalence.precoherent_isSheaf_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Precoherent C] (A : Type u_3)
  [inst_3 : CategoryTheory.Category.{v_3, u_3} A] (e : C ≌ D) (F : CategoryTheory.Functor Cᵒᵖ A),
  CategoryTheory.Presheaf.IsSheaf (CategoryTheory.coherentTopology C) F ↔
    CategoryTheory.Presheaf.IsSheaf (CategoryTheory.coherentTopology D) (e.inverse.op.comp F)

The coherent sheaf condition can be checked after precomposing with the equivalence.

Defined in

Mathlib.CategoryTheory.Sites.Coherent.Equivalence

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PrecoherentCategoryTheory.Category