Theorems · Theorem · category theory

CategoryTheory.Functor.IsCoverDense.isContinuous

∀ {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] (J : CategoryTheory.GrothendieckTopology C)
  (K : CategoryTheory.GrothendieckTopology D) (G : CategoryTheory.Functor C D) [G.IsCoverDense K] [G.IsLocallyFull K]
  [G.IsLocallyFaithful K], CategoryTheory.CoverPreserving J K G → G.IsContinuous J K

Defined in: Mathlib.CategoryTheory.Sites.DenseSubsite.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsCoverDense CategoryTheory.Functor.IsLocallyFull CategoryTheory.Functor.IsLocallyFaithful

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
CategoryTheory.Functor.IsContinuousstatement · cited by 100
CategoryTheory.Functor.IsCoverDensestatement and proof · cited by 60
CategoryTheory.Functor.IsLocallyFullstatement and proof · cited by 54
CategoryTheory.CoverPreservingstatement and proof · cited by 32
CategoryTheory.Functor.IsLocallyFaithfulstatement and proof · cited by 13
CategoryTheory.Functor.isContinuous_of_coverPreservingproof · cited by 4
CategoryTheory.Functor.IsCoverDense.compatiblePreservingproof · cited by 1

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