Theorems · Inductive type · category theory
HomotopicalAlgebra.Cylinder
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → [HomotopicalAlgebra.CategoryWithWeakEquivalences C] → C → Type (max u v)In a category with weak equivalences, a cylinder is the
data of a weak equivalence π : I ⟶ A equipped with two sections
- Cited by
- 31 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 by56
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.Cylinder.toPrecylinderstatement and proof · cited by 23
- HomotopicalAlgebra.LeftHomotopyRelproof · cited by 22
- HomotopicalAlgebra.Cylinder.LeftHomotopystatement and proof · cited by 13
- HomotopicalAlgebra.Cylinder.IsGoodstatement · cited by 11
- HomotopicalAlgebra.Cylinder.IsVeryGoodstatement · cited by 6
- HomotopicalAlgebra.Cylinder.ofFactorizationDatastatement · cited by 6
- HomotopicalAlgebra.Cylinder.symmstatement and proof · cited by 6
- HomotopicalAlgebra.Cylinder.transstatement and proof · cited by 4
- HomotopicalAlgebra.LeftHomotopyRel.exists_good_cylinderstatement and proof · cited by 3
- HomotopicalAlgebra.Cylinder.LeftHomotopy.leftHomotopyRelstatement and proof · cited by 3
- HomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinderstatement and proof · cited by 2