Theorems · Inductive type · category theory
CategoryTheory.HomRel.CompClosure
{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → HomRel C → HomRel CGenerates the closure of a family of relations w.r.t. composition from left and right.
- Defined in
- Mathlib.CategoryTheory.Quotient
- Cited by
- 19 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 by34
Results whose statement or proof uses this declaration.
- CategoryTheory.Quotient.functorproof · cited by 41
- CategoryTheory.Quotient.soundproof · cited by 16
- Quiver.FreeGroupoid.ofproof · cited by 7
- CategoryTheory.HomRel.compClosure_eq_selfstatement · cited by 4
- CategoryTheory.Quotient.functor_homRel_eq_compClosure_eqvGenstatement · cited by 4
- HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRightproof · cited by 4
- CategoryTheory.Quotient.lift_uniqueproof · cited by 3
- CategoryTheory.toQuotientPathsproof · cited by 2
- CategoryTheory.HomRel.CompClosure.casesOnstatement and proof · cited by 2
- CategoryTheory.Quotient.Homproof · cited by 1
- CategoryTheory.HomRel.CompClosure.ofstatement and proof · cited by 1
- Quiver.FreeGroupoid.congr_comp_reversestatement and proof · cited by 1