Theorems · Theorem · category theory
HomotopicalAlgebra.bijective_leftHomotopyClassToHom_iff_bijective_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)
[inst_3 : L.IsLocalization (HomotopicalAlgebra.weakEquivalences C)] (X Y : C) [HomotopicalAlgebra.IsCofibrant X]
[HomotopicalAlgebra.IsFibrant Y],
Function.Bijective (HomotopicalAlgebra.leftHomotopyClassToHom L) ↔
Function.Bijective (HomotopicalAlgebra.rightHomotopyClassToHom L)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · 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
- Function.Bijectivestatement and proof · cited by 863
- CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
- HomotopicalAlgebra.IsFibrantstatement and proof · cited by 56
- HomotopicalAlgebra.weakEquivalencesstatement and proof · cited by 44
Cited by1
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.bijective_leftHomotopyClassToHomproof · cited by 2