Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.HasQuotient.iff_of_eqvGen
∀ {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] [W.HasQuotient homRel] {X Y : C} {f g : X ⟶ Y},
Relation.EqvGen homRel f g → (W f ↔ W g)- Cited by
- 1 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.
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.MorphismPropertystatement and proof · cited by 2,179
- HomRelstatement and proof · cited by 49
- Relation.EqvGenstatement and proof · cited by 49
- CategoryTheory.HomRel.IsStableUnderPrecompstatement and proof · cited by 7
- CategoryTheory.HomRel.IsStableUnderPostcompstatement and proof · cited by 7
- CategoryTheory.MorphismProperty.HasQuotientstatement and proof · cited by 4
- CategoryTheory.MorphismProperty.HasQuotient.iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.quotient_iffproof · cited by 3