Theorems · Theorem · category theory
CategoryTheory.HomRel.compClosure_iff_self
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (r : HomRel C)
[CategoryTheory.HomRel.IsStableUnderPrecomp r] [CategoryTheory.HomRel.IsStableUnderPostcomp r] {X Y : C}
(f g : X ⟶ Y), CategoryTheory.HomRel.CompClosure r f g ↔ r f g- Defined in
- Mathlib.CategoryTheory.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.CategoryStruct.compproof · cited by 17,999
- HomRelstatement and proof · cited by 49
- CategoryTheory.HomRel.CompClosurestatement and proof · cited by 19
- CategoryTheory.HomRel.IsStableUnderPostcompstatement and proof · cited by 7
- CategoryTheory.HomRel.IsStableUnderPrecompstatement and proof · cited by 7
- CategoryTheory.HomRel.CompClosure.casesOnproof · cited by 2
- CategoryTheory.HomRel.CompClosure.ofproof · cited by 1
- CategoryTheory.HomRel.IsStableUnderPostcomp.comp_rightproof · cited by 1
- CategoryTheory.HomRel.IsStableUnderPrecomp.comp_leftproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.