Theorems · Inductive type · category theory
HomotopicalAlgebra.PathObject
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → [HomotopicalAlgebra.CategoryWithWeakEquivalences C] → C → Type (max u v)In a category with weak equivalences, a path object is the
data of a weak equivalence ι : A ⟶ P equipped with two retractions.
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
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
- HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement · cited by 77
Cited by57
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.PathObject.toPrepathObjectstatement and proof · cited by 24
- HomotopicalAlgebra.RightHomotopyRelproof · cited by 22
- HomotopicalAlgebra.PathObject.RightHomotopystatement and proof · cited by 14
- HomotopicalAlgebra.PathObject.IsGoodstatement · cited by 11
- HomotopicalAlgebra.PathObject.IsVeryGoodstatement · cited by 7
- HomotopicalAlgebra.PathObject.ofFactorizationDatastatement · cited by 6
- HomotopicalAlgebra.PathObject.symmstatement and proof · cited by 6
- HomotopicalAlgebra.PathObject.transstatement and proof · cited by 4
- HomotopicalAlgebra.PathObject.RightHomotopy.rightHomotopyRelstatement and proof · cited by 3
- HomotopicalAlgebra.RightHomotopyRel.exists_good_pathObjectstatement and proof · cited by 3
- HomotopicalAlgebra.RightHomotopyRel.exists_very_good_pathObjectstatement and proof · cited by 3