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Theorems · Definition · category theory

HomotopicalAlgebra.RightHomotopyClass.mk

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] → (X ⟶ Y) → HomotopicalAlgebra.RightHomotopyClass X Y

Given f : X ⟶ Y, this is the class of f in the quotient RightHomotopyClass X Y.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy
Cited by
17 results in Mathlib
Foundations
Depth 7 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.RightHomotopyClass.mk_eq_mk_iff · cited by 5RightHomotopyClass.mk_eq_…HomotopicalAlgebra.RightHomotopyClass.precomp · cited by 5RightHomotopyClass.precompHomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass · cited by 4HomotopicalAlgebra.leftHo…HomotopicalAlgebra.RightHomotopyClass.mk_surjective · cited by 4RightHomotopyClass.mk_sur…HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalence · cited by 4RightHomotopyClass.precom…HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight · cited by 4HoCat.homEquivRightHomotopicalAlgebra.bijective_rightHomotopyClassToHom · cited by 2HomotopicalAlgebra.biject…HomotopicalAlgebra.RightHomotopyClass.whitehead · cited by 2RightHomotopyClass.whiteh…HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_weakEquivalence · cited by 1RightHomotopyClass.precom…HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_mk · cited by 0HomotopicalAlgebra.leftHo…HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_symm_mk · cited by 0HomotopicalAlgebra.leftHo…HomotopicalAlgebra.CofibrantObject.bifibrantResolutionObj_hom_ext · cited by 0CofibrantObject.bifibrant…HomotopicalAlgebra.rightHomotopyClassToHom_mk · cited by 0HomotopicalAlgebra.rightH…HomotopicalAlgebra.RightHomotopyClass.precomp_mk · cited by 0RightHomotopyClass.precom…HomotopicalAlgebra.RightHomotopyClass.sound · cited by 0RightHomotopyClass.soundCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomHomotopicalAlgebra.CategoryWithWeakEquivalences · cited by 77HomotopicalAlgebra.Catego…HomotopicalAlgebra.RightHomotopyRel · cited by 22HomotopicalAlgebra.RightH…HomotopicalAlgebra.RightHomotopyClass · cited by 16HomotopicalAlgebra.RightH…RightHomotopyClass.mkCITED BYCITES

Cites5

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Cited by20

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