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Theorems · Definition · category theory

HomotopicalAlgebra.RightHomotopyRel

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

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

Defined in
Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy
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.BifibrantObject.homRel · cited by 22BifibrantObject.homRelHomotopicalAlgebra.CofibrantObject.homRel · cited by 20CofibrantObject.homRelHomotopicalAlgebra.RightHomotopyClass.mk · cited by 17RightHomotopyClass.mkHomotopicalAlgebra.RightHomotopyClass · cited by 16HomotopicalAlgebra.RightH…HomotopicalAlgebra.RightHomotopyClass.mk_eq_mk_iff · cited by 5RightHomotopyClass.mk_eq_…HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass · cited by 4HomotopicalAlgebra.leftHo…HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight · cited by 4HoCat.homEquivRightHomotopicalAlgebra.PathObject.RightHomotopy.rightHomotopyRel · cited by 3RightHomotopy.rightHomoto…HomotopicalAlgebra.RightHomotopyRel.exists_good_pathObject · cited by 3RightHomotopyRel.exists_g…HomotopicalAlgebra.RightHomotopyRel.exists_very_good_pathObject · cited by 3RightHomotopyRel.exists_v…HomotopicalAlgebra.leftHomotopyRel_iff_rightHomotopyRel · cited by 2HomotopicalAlgebra.leftHo…HomotopicalAlgebra.CofibrantObject.homRel_iff_rightHomotopyRel · cited by 2CofibrantObject.homRel_if…HomotopicalAlgebra.BifibrantObject.homRel_iff_rightHomotopyRel · cited by 2BifibrantObject.homRel_if…HomotopicalAlgebra.RightHomotopyClass.whitehead · cited by 2RightHomotopyClass.whiteh…HomotopicalAlgebra.RightHomotopyRel.equivalence · cited by 2RightHomotopyRel.equivale…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomHomotopicalAlgebra.CategoryWithWeakEquivalences · cited by 77HomotopicalAlgebra.Catego…HomRel · cited by 49HomRelHomotopicalAlgebra.PathObject · cited by 32HomotopicalAlgebra.PathOb…HomotopicalAlgebra.PathObject.RightHomotopy · cited by 14PathObject.RightHomotopyHomotopicalAlgebra.RightHomot…CITED BYCITES

Cites6

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

Cited by30

Results whose statement or proof uses this declaration.