Theorems · Theorem · category theory

CategoryTheory.LocalizerMorphism.essSurj_of_hasLeftResolutions

∀ {C₁ : Type u_1} {C₂ : Type u_2} {D₂ : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] [inst_2 : CategoryTheory.Category.{v_4, u_4} D₂]
  {W₁ : CategoryTheory.MorphismProperty C₁} {W₂ : CategoryTheory.MorphismProperty C₂}
  (Φ : CategoryTheory.LocalizerMorphism W₁ W₂) (L₂ : CategoryTheory.Functor C₂ D₂) [L₂.IsLocalization W₂]
  [Φ.HasLeftResolutions], (Φ.functor.comp L₂).EssSurj

Defined in: Mathlib.CategoryTheory.Localization.Resolution
Cited by: 1 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsLocalization CategoryTheory.LocalizerMorphism.HasLeftResolutions

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites19

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.Functor.compstatement · cited by 6,529
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Iso.transproof · cited by 566
CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
CategoryTheory.LocalizerMorphismstatement and proof · cited by 161
Classical.arbitraryproof · cited by 161
CategoryTheory.LocalizerMorphism.functorstatement · cited by 140
CategoryTheory.Functor.EssSurjstatement and proof · cited by 88
CategoryTheory.Functor.objObjPreimageIsoproof · cited by 54
CategoryTheory.Functor.objPreimageproof · cited by 49

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.LocalizerMorphism.isIso_iff_of_hasLeftResolutionsproof · cited by 0