Theorems · Theorem · category theory

CategoryTheory.Functor.IsDenseSubsite.isLocallyFull

∀ {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)
  [CategoryTheory.Functor.IsDenseSubsite J K G], G.IsLocallyFull K

Defined in: Mathlib.CategoryTheory.Sites.DenseSubsite.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 4 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsDenseSubsite

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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.IsDenseSubsitestatement and proof · cited by 87
CategoryTheory.Functor.IsLocallyFullstatement · cited by 54
CategoryTheory.Functor.IsDenseSubsite.isLocallyFull'proof · cited by 1

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_rightproof · cited by 1
CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_leftproof · cited by 1
CategoryTheory.Functor.OneHypercoverDenseData.sieve_memproof · cited by 0