Theorems · Theorem · category theory
CategoryTheory.Localization.inverts
∀ {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], W.IsInvertedBy L- Cited by
- 63 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
- CategoryTheory.MorphismProperty.IsInvertedBystatement · cited by 118
- CategoryTheory.Functor.IsLocalization.invertsproof · cited by 2
Cited by66
Results whose statement or proof uses this declaration.
- CategoryTheory.Localization.exists_leftFractionstatement and proof · cited by 14
- CategoryTheory.Localization.Preadditive.add'proof · cited by 14
- CategoryTheory.Functor.IsLocalization.of_equivalence_targetproof · cited by 8
- CategoryTheory.Localization.exists_leftFraction₂statement and proof · cited by 7
- CategoryTheory.Localization.Preadditive.add'_eqstatement and proof · cited by 7
- CategoryTheory.Localization.exists_rightFractionstatement and proof · cited by 5
- CategoryTheory.Localization.essSurj_mapArrowproof · cited by 4
- CategoryTheory.MorphismProperty.LeftFraction.map_eq_iffstatement and proof · cited by 4
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernelproof · cited by 3
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernelproof · cited by 3
- CategoryTheory.MorphismProperty.map_eq_iff_precompproof · cited by 3
- CategoryTheory.Localization.equivalenceFromModelproof · cited by 3