Theorems · Theorem · category theory
HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C]
{X₁ X₂ : HomotopicalAlgebra.CofibrantObject C} (f : X₁ ⟶ X₂),
CategoryTheory.CategoryStruct.comp X₁.iBifibrantResolutionObj
(HomotopicalAlgebra.CofibrantObject.homMk (HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap f).hom) =
CategoryTheory.CategoryStruct.comp f X₂.iBifibrantResolutionObj- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- CategoryTheory.InducedCategory.Hom.homstatement · cited by 850
- CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- HomotopicalAlgebra.BifibrantObjectstatement · cited by 38
- HomotopicalAlgebra.bifibrantObjectsstatement · cited by 37
- HomotopicalAlgebra.CofibrantObjectstatement and proof · cited by 35
- HomotopicalAlgebra.cofibrantObjectsstatement · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac'proof · cited by 1
- HomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac_assocproof · cited by 0