Theorems · Theorem · category theory

CategoryTheory.regularTopology.exists_effectiveEpi_iff_mem_induced

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (F : CategoryTheory.Functor C D) [F.PreservesEffectiveEpis]
  [F.ReflectsEffectiveEpis] [F.Full] [F.Faithful] [F.EffectivelyEnough] [inst_7 : CategoryTheory.Preregular D] (X : C)
  (S : CategoryTheory.Sieve X),
  (∃ Y π, CategoryTheory.EffectiveEpi π ∧ S.arrows π) ↔ S ∈ (F.inducedTopology (CategoryTheory.regularTopology D)) X

Defined in

Mathlib.CategoryTheory.Sites.Coherent.SheafComparison

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.PreservesEffectiveEpisCategoryTheory.Functor.ReflectsEffectiveEpisCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.Functor.EffectivelyEnoughCategoryTheory.Preregular