Theorems · Theorem · category theory

HomotopicalAlgebra.CofibrantBrownFactorization.s_p_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
  {f : X ⟶ Y} (self : HomotopicalAlgebra.CofibrantBrownFactorization f) {Z : C} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp self.s (CategoryTheory.CategoryStruct.comp self.p h) = h

Defined in: Mathlib.AlgebraicTopology.ModelCategory.BrownLemma
Cited by: 1 results in Mathlib
Foundations: Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory

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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.compstatement · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Category.id_compproof · cited by 1,998
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
CategoryTheory.MorphismProperty.MapFactorizationData.Zstatement · cited by 63
HomotopicalAlgebra.cofibrationsstatement · cited by 37
CategoryTheory.MorphismProperty.MapFactorizationData.pstatement and proof · cited by 36
HomotopicalAlgebra.trivialFibrationsstatement · cited by 30
HomotopicalAlgebra.CofibrantBrownFactorizationstatement and proof · cited by 6
HomotopicalAlgebra.CofibrantBrownFactorization.toMapFactorizationDatastatement and proof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_weakEquivalenceproof · cited by 1