Theorems · Theorem · category theory
HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_mk
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
[inst_2 : HomotopicalAlgebra.IsCofibrant X] [inst_3 : HomotopicalAlgebra.IsFibrant Y] (f : X ⟶ Y),
HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass (HomotopicalAlgebra.LeftHomotopyClass.mk f) =
HomotopicalAlgebra.RightHomotopyClass.mk f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- Equivstatement · cited by 8,337
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
- HomotopicalAlgebra.IsFibrantstatement and proof · cited by 56
- HomotopicalAlgebra.RightHomotopyClass.mkstatement · cited by 17
- HomotopicalAlgebra.RightHomotopyClassstatement · cited by 16
- HomotopicalAlgebra.LeftHomotopyClassstatement · cited by 15
- HomotopicalAlgebra.LeftHomotopyClass.mkstatement · cited by 14
- HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClassstatement · cited by 4
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