Theorems · Theorem · category theory
HomotopicalAlgebra.CofibrantObject.exists_bifibrant
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C]
(X : HomotopicalAlgebra.CofibrantObject C),
∃ Y i,
HomotopicalAlgebra.Cofibration (HomotopicalAlgebra.CofibrantObject.ι.map i) ∧
HomotopicalAlgebra.WeakEquivalence (HomotopicalAlgebra.CofibrantObject.ι.map i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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.Functor.mapstatement · cited by 8,698
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- CategoryTheory.Limits.terminalproof · cited by 141
- CategoryTheory.Limits.terminal.fromproof · cited by 77
- CategoryTheory.MorphismProperty.MapFactorizationData.Zproof · cited by 63
- CategoryTheory.MorphismProperty.MapFactorizationDataproof · cited by 63
- HomotopicalAlgebra.IsCofibrantproof · cited by 56
- HomotopicalAlgebra.IsFibrantproof · cited by 56
Cited by1
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.CofibrantObject.bifibrantResolutionObjproof · cited by 13