Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.quotient_iff
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (W : CategoryTheory.MorphismProperty C)
(homRel : HomRel C) [inst_1 : CategoryTheory.HomRel.IsStableUnderPrecomp homRel]
[inst_2 : CategoryTheory.HomRel.IsStableUnderPostcomp homRel] [inst_3 : W.HasQuotient homRel] {X Y : C} (f : X ⟶ Y),
W.quotient homRel ((CategoryTheory.Quotient.functor homRel).map f) ↔ W f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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 and proof · cited by 19,642
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- Relation.EqvGenproof · cited by 49
- HomRelstatement and proof · cited by 49
- CategoryTheory.Quotientstatement · cited by 48
- CategoryTheory.Quotient.asproof · cited by 47
- CategoryTheory.Quotient.functorstatement and proof · cited by 41
- CategoryTheory.HomRel.IsStableUnderPostcompstatement and proof · cited by 7
- CategoryTheory.HomRel.IsStableUnderPrecompstatement and proof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.CofibrantObject.weakEquivalence_toHoCat_map_iffproof · cited by 0
- CategoryTheory.MorphismProperty.eq_inverseImage_quotientFunctorproof · cited by 0
- HomotopicalAlgebra.FibrantObject.weakEquivalence_toHoCat_map_iffproof · cited by 0