Theorems · Theorem · algebraic topology

AlgebraicTopology.DoldKan.P_f_idem_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {X : CategoryTheory.SimplicialObject C} (q n : ℕ) {Z : C}
  (h : (AlgebraicTopology.AlternatingFaceMapComplex.obj X).X n ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((AlgebraicTopology.DoldKan.P q).f n)
      (CategoryTheory.CategoryStruct.comp ((AlgebraicTopology.DoldKan.P q).f n) h) =
    CategoryTheory.CategoryStruct.comp ((AlgebraicTopology.DoldKan.P q).f n) h

Defined in: Mathlib.AlgebraicTopology.DoldKan.Projections
Cited by: 0 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Preadditivestatement and proof · cited by 3,309
HomologicalComplex.Xstatement and proof · cited by 1,839
HomologicalComplex.Hom.fstatement and proof · cited by 845
ComplexShape.downstatement · cited by 605
CategoryTheory.SimplicialObjectstatement and proof · cited by 548
AlgebraicTopology.AlternatingFaceMapComplex.objstatement and proof · cited by 146
AlgebraicTopology.DoldKan.Pstatement and proof · cited by 38
AlgebraicTopology.DoldKan.P_f_idemproof · cited by 5

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