Theorems · Inductive type · category theory
CategoryTheory.HomRel.IsStableUnderPrecomp
{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → HomRel C → PropThe condition that a HomRel is stable under precomposition.
- Defined in
- Mathlib.CategoryTheory.Quotient
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- HomRelstatement · cited by 49
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.HomRel.compClosure_eq_selfstatement and proof · cited by 4
- CategoryTheory.MorphismProperty.HasQuotientstatement · cited by 4
- CategoryTheory.MorphismProperty.quotient_iffstatement and proof · cited by 3
- CategoryTheory.MorphismProperty.quotientstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.HasQuotient.iffstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.HasQuotient.iff_of_eqvGenstatement and proof · cited by 1
- CategoryTheory.HomRel.IsStableUnderPrecomp.comp_leftstatement and proof · cited by 1
- CategoryTheory.Congruence.casesOnstatement and proof · cited by 0
- CategoryTheory.Congruence.recOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.HasQuotient.casesOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.HasQuotient.recOnstatement and proof · cited by 0
- CategoryTheory.HomRel.compClosure_iff_selfstatement and proof · cited by 0