Theorems · Theorem · category theory
HomotopicalAlgebra.bijective_leftHomotopyClassToHom
∀ {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)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Function.Bijectivestatement · 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
- HomotopicalAlgebra.LeftHomotopyClassstatement · cited by 15
- HomotopicalAlgebra.leftHomotopyClassToHomstatement · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.LeftHomotopyRel.iff_map_eqproof · cited by 0
- HomotopicalAlgebra.map_surjective_of_isLocalizationproof · cited by 0