Theorems · Definition · category theory
HomotopicalAlgebra.rightHomotopyClassToHom
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : HomotopicalAlgebra.ModelCategory C] →
{H : Type u_2} →
[inst_2 : CategoryTheory.Category.{v_2, u_2} H] →
(L : CategoryTheory.Functor C H) →
[L.IsLocalization (HomotopicalAlgebra.weakEquivalences C)] →
{X Y : C} → HomotopicalAlgebra.RightHomotopyClass X Y → (L.obj X ⟶ L.obj Y)The map RightHomotopyClass X Y → (L.obj X ⟶ L.obj Y) when L is
a localization functor with respect to weakEquivalences C.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- HomotopicalAlgebra.weakEquivalencesstatement and proof · cited by 44
- HomotopicalAlgebra.RightHomotopyClassstatement · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.bijective_rightHomotopyClassToHomstatement and proof · cited by 2
- HomotopicalAlgebra.bijective_leftHomotopyClassToHom_iff_bijective_rightHomotopyClassToHomstatement and proof · cited by 1
- HomotopicalAlgebra.rightHomotopyClassToHom.congr_simpstatement and proof · cited by 0
- HomotopicalAlgebra.rightHomotopyClassToHom_mkstatement · cited by 0