Theorems · Theorem · category theory
CategoryTheory.AreEqualizedByLocalization.map_eq
∀ {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] {W : CategoryTheory.MorphismProperty C} {X Y : C} {f g : X ⟶ Y},
CategoryTheory.AreEqualizedByLocalization W f g →
∀ (L : CategoryTheory.Functor C D) [L.IsLocalization W], L.map f = L.map g- Cited by
- 4 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
- CategoryTheory.areEqualizedByLocalization_iffproof · cited by 6
- CategoryTheory.AreEqualizedByLocalizationstatement and proof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- HomologicalComplexUpToQuasiIso.Q_map_eq_of_homotopyproof · cited by 1
- HomotopicalAlgebra.RightHomotopyRel.iff_map_eqproof · cited by 0
- HomotopicalAlgebra.LeftHomotopyRel.iff_map_eqproof · cited by 0
- CategoryTheory.AreEqualizedByLocalization.map_eq_of_isInvertedByproof · cited by 0