Theorems · Theorem · category theory
HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalence
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C} (Z : C)
[HomotopicalAlgebra.IsFibrant Z] (f : X ⟶ Y) [HomotopicalAlgebra.Cofibration f]
[HomotopicalAlgebra.WeakEquivalence f], Function.Bijective fun g => g.precomp f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites44
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- Function.Bijectivestatement · cited by 863
- CategoryTheory.Limits.limit.lift_πproof · cited by 266
- CategoryTheory.Limits.prod.fstproof · cited by 189
- CategoryTheory.Limits.prod.sndproof · cited by 185
- CategoryTheory.CommSqproof · cited by 158
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- CategoryTheory.Limits.prod.liftproof · cited by 123
- CategoryTheory.Limits.BinaryFan.mkproof · cited by 112
Cited by4
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.bijective_rightHomotopyClassToHomproof · cited by 2
- HomotopicalAlgebra.CofibrantObject.bifibrantResolutionObj_hom_extproof · cited by 0
- HomotopicalAlgebra.FibrantObject.HoCat.resolutionObj_hom_extproof · cited by 0