Theorems · Theorem · category theory

CategoryTheory.Functor.coverPreserving_restrictedTopology

∀ {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] (G : CategoryTheory.Functor C D)
  (K : CategoryTheory.GrothendieckTopology D) [G.LocallyCoverDense K] [G.IsLocallyFull K] [G.IsLocallyFaithful K],
  CategoryTheory.CoverPreserving (G.restrictedTopology K) K G

If G is locally fully faithful and locally cover dense, G is cover-preserving w.r.t. the restricted topology.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology

Cited by

3 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.LocallyCoverDenseCategoryTheory.Functor.IsLocallyFullCategoryTheory.Functor.IsLocallyFaithful