Theorems · Definition · category theory
HomotopicalAlgebra.LeftHomotopyRel
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → [HomotopicalAlgebra.CategoryWithWeakEquivalences C] → HomRel CThe left homotopy relation on morphisms in a category with weak equivalences.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
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
- HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
- HomRelstatement · cited by 49
- HomotopicalAlgebra.Cylinderproof · cited by 31
- HomotopicalAlgebra.Cylinder.LeftHomotopyproof · cited by 13
Cited by28
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.LeftHomotopyClassproof · cited by 15
- HomotopicalAlgebra.LeftHomotopyClass.mkproof · cited by 14
- HomotopicalAlgebra.FibrantObject.homRelproof · cited by 12
- HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClassproof · cited by 4
- HomotopicalAlgebra.Cylinder.LeftHomotopy.leftHomotopyRelstatement · cited by 3
- HomotopicalAlgebra.LeftHomotopyClass.mk_eq_mk_iffstatement · cited by 3
- HomotopicalAlgebra.LeftHomotopyRel.exists_good_cylinderstatement and proof · cited by 3
- HomotopicalAlgebra.RightHomotopyClass.whiteheadproof · cited by 2
- HomotopicalAlgebra.leftHomotopyRel_iff_rightHomotopyRelstatement and proof · cited by 2
- HomotopicalAlgebra.LeftHomotopyRel.equivalencestatement and proof · cited by 2
- HomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinderstatement and proof · cited by 2
- HomotopicalAlgebra.LeftHomotopyRel.rightHomotopyRelstatement and proof · cited by 2