Theorems · Theorem · category theory
CategoryTheory.HomRel.compClosure_eq_self
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (r : HomRel C)
[CategoryTheory.HomRel.IsStableUnderPrecomp r] [CategoryTheory.HomRel.IsStableUnderPostcomp r],
CategoryTheory.HomRel.CompClosure r = r- Defined in
- Mathlib.CategoryTheory.Quotient
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Homproof · cited by 32,603
- HomRelstatement and proof · cited by 49
- CategoryTheory.HomRel.CompClosurestatement · cited by 19
- CategoryTheory.HomRel.IsStableUnderPostcompstatement and proof · cited by 7
- CategoryTheory.HomRel.IsStableUnderPrecompstatement and proof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.quotient_iffproof · cited by 3
- CategoryTheory.Quotient.functor_map_eq_iffproof · cited by 2
- HomotopicalAlgebra.CofibrantObject.toHoCat_map_eq_iffproof · cited by 1
- HomotopicalAlgebra.FibrantObject.toHoCat_map_eq_iffproof · cited by 0