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Theorems · Definition · category theory

HomotopicalAlgebra.LeftHomotopyRel

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] → [HomotopicalAlgebra.CategoryWithWeakEquivalences C] → HomRel C

The left homotopy relation on morphisms in a category with weak equivalences.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy
Cited by
22 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithWeakEquivalences

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomotopicalAlgebra.LeftHomotopyClass · cited by 15HomotopicalAlgebra.LeftHo…HomotopicalAlgebra.LeftHomotopyClass.mk · cited by 14LeftHomotopyClass.mkHomotopicalAlgebra.FibrantObject.homRel · cited by 12FibrantObject.homRelHomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass · cited by 4HomotopicalAlgebra.leftHo…HomotopicalAlgebra.Cylinder.LeftHomotopy.leftHomotopyRel · cited by 3LeftHomotopy.leftHomotopy…HomotopicalAlgebra.LeftHomotopyClass.mk_eq_mk_iff · cited by 3LeftHomotopyClass.mk_eq_m…HomotopicalAlgebra.LeftHomotopyRel.exists_good_cylinder · cited by 3LeftHomotopyRel.exists_go…HomotopicalAlgebra.RightHomotopyClass.whitehead · cited by 2RightHomotopyClass.whiteh…HomotopicalAlgebra.leftHomotopyRel_iff_rightHomotopyRel · cited by 2HomotopicalAlgebra.leftHo…HomotopicalAlgebra.LeftHomotopyRel.equivalence · cited by 2LeftHomotopyRel.equivalen…HomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinder · cited by 2LeftHomotopyRel.exists_ve…HomotopicalAlgebra.LeftHomotopyRel.rightHomotopyRel · cited by 2LeftHomotopyRel.rightHomo…HomotopicalAlgebra.RightHomotopyRel.leftHomotopyRel · cited by 2RightHomotopyRel.leftHomo…HomotopicalAlgebra.FibrantObject.homRel_iff_leftHomotopyRel · cited by 1FibrantObject.homRel_iff_…HomotopicalAlgebra.LeftHomotopyRel.factorsThroughLocalization · cited by 1LeftHomotopyRel.factorsTh…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomHomotopicalAlgebra.CategoryWithWeakEquivalences · cited by 77HomotopicalAlgebra.Catego…HomRel · cited by 49HomRelHomotopicalAlgebra.Cylinder · cited by 31HomotopicalAlgebra.Cylind…HomotopicalAlgebra.Cylinder.LeftHomotopy · cited by 13Cylinder.LeftHomotopyHomotopicalAlgebra.LeftHomoto…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by28

Results whose statement or proof uses this declaration.