Theorems · Theorem · category theory

CategoryTheory.coherentTopology.eq_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)
  [inst_2 : F.PreservesFiniteEffectiveEpiFamilies] [inst_3 : F.ReflectsFiniteEffectiveEpiFamilies] [inst_4 : F.Full]
  [inst_5 : F.Faithful] [inst_6 : F.EffectivelyEnough] [inst_7 : CategoryTheory.Precoherent D],
  CategoryTheory.coherentTopology C = F.inducedTopology (CategoryTheory.coherentTopology D)

Defined in

Mathlib.CategoryTheory.Sites.Coherent.SheafComparison

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.PreservesFiniteEffectiveEpiFamiliesCategoryTheory.Functor.ReflectsFiniteEffectiveEpiFamiliesCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.Functor.EffectivelyEnoughCategoryTheory.Precoherent