Theorems · Inductive type · category theory
HomotopicalAlgebra.Cylinder.IsGood
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{A : C} →
[inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] →
HomotopicalAlgebra.Cylinder A →
[CategoryTheory.Limits.HasBinaryCoproduct A A] → [HomotopicalAlgebra.CategoryWithCofibrations C] → PropA cylinder object P is good if the morphism
P.i : A ⨿ A ⟶ P.I is a cofibration.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Limits.HasBinaryCoproductstatement · cited by 81
- HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement · cited by 77
- HomotopicalAlgebra.CategoryWithCofibrationsstatement · cited by 46
- HomotopicalAlgebra.Cylinderstatement · cited by 31
Cited by20
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.Cylinder.transstatement and proof · cited by 4
- HomotopicalAlgebra.LeftHomotopyRel.exists_good_cylinderstatement · cited by 3
- HomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinderproof · cited by 2
- HomotopicalAlgebra.LeftHomotopyRel.rightHomotopyproof · cited by 1
- HomotopicalAlgebra.RightHomotopyRel.leftHomotopystatement and proof · cited by 1
- HomotopicalAlgebra.LeftHomotopyRel.transproof · cited by 1
- HomotopicalAlgebra.Cylinder.LeftHomotopy.exists_good_cylinderstatement · cited by 1
- HomotopicalAlgebra.Cylinder.LeftHomotopy.transstatement and proof · cited by 1
- HomotopicalAlgebra.Cylinder.trans_i₀statement and proof · cited by 0
- HomotopicalAlgebra.Cylinder.trans_i₁statement and proof · cited by 0
- HomotopicalAlgebra.Cylinder.trans_πstatement and proof · cited by 0