Theorems · Theorem · category theory
CategoryTheory.Localization.essSurj
∀ {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] (L : CategoryTheory.Functor C D)
(W : CategoryTheory.MorphismProperty C) [L.IsLocalization W], L.EssSurj- Cited by
- 16 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Equivalence.inverseproof · cited by 1,130
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.Equivalence.counitIsoproof · cited by 480
- CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
- CategoryTheory.Iso.appproof · cited by 253
- Equiv.invFunproof · cited by 163
- CategoryTheory.Functor.EssSurjstatement · cited by 88
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.Localization.natTrans_extproof · cited by 7
- CategoryTheory.Localization.essSurj_mapArrowproof · cited by 4
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernelproof · cited by 3
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernelproof · cited by 3
- CategoryTheory.LocalizerMorphism.essSurj_of_hasRightResolutionsproof · cited by 2
- CategoryTheory.Localization.Preadditive.addCommGroupproof · cited by 2
- CategoryTheory.Functor.isPointwiseLeftKanExtensionOfIsoOfIsLocalizationproof · cited by 2
- CategoryTheory.Localization.functor_additive_iffproof · cited by 2
- CategoryTheory.Functor.isPointwiseRightKanExtensionOfIsoOfIsLocalizationproof · cited by 2
- CategoryTheory.Functor.faithful_of_comp_of_hasLeftCalculusOfFractionsproof · cited by 1
- CategoryTheory.LocalizerMorphism.essSurj_of_hasLeftResolutionsproof · cited by 1
- CategoryTheory.ObjectProperty.SerreClassLocalization.epi_map_tfaeproof · cited by 1