Theorems · Definition · category theory

HomotopicalAlgebra.FibrantBrownFactorization.r

{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.FibrantBrownFactorization f) → self.Z ⟶ X

a fibration that is a retraction of i

Defined in: Mathlib.AlgebraicTopology.ModelCategory.BrownLemma
Cited by: 4 results in Mathlib
Foundations: Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

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
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
CategoryTheory.MorphismProperty.MapFactorizationData.Zstatement · cited by 63
HomotopicalAlgebra.fibrationsstatement · cited by 40
HomotopicalAlgebra.trivialCofibrationsstatement · cited by 31
HomotopicalAlgebra.FibrantBrownFactorizationstatement and proof · cited by 6
HomotopicalAlgebra.FibrantBrownFactorization.toMapFactorizationDatastatement · cited by 6

Cited by4

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.FibrantBrownFactorization.i_rstatement · cited by 2
HomotopicalAlgebra.FibrantBrownFactorization.mk'_rstatement and proof · cited by 0
HomotopicalAlgebra.LeftHomotopyClass.postcomp_bijective_of_weakEquivalenceproof · cited by 0
HomotopicalAlgebra.FibrantBrownFactorization.i_r_assocstatement and proof · cited by 0