Theorems · Theorem · algebraic topology

CategoryTheory.SimplicialObject.Splitting.fromNondegComplex_f

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X : CategoryTheory.SimplicialObject C} (s : X.Splitting)
  [inst_1 : CategoryTheory.Preadditive C] (n : ℕ),
  s.fromNondegComplex.f n = CategoryTheory.CategoryStruct.comp (s.ι n) (AlgebraicTopology.DoldKan.PInfty.f n)

Defined in: Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject
Cited by: 1 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites21

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.CategoryStruct.compstatement and proof · cited by 17,999
Oppositestatement · cited by 8,081
CategoryTheory.Preadditivestatement and proof · cited by 3,309
SimplexCategorystatement · cited by 2,204
CategoryTheory.Category.comp_idproof · cited by 2,119
HomologicalComplex.Xstatement · cited by 1,839
HomologicalComplex.Hom.fstatement and proof · cited by 845
CategoryTheory.Functor.map_idproof · cited by 616
ComplexShape.downstatement · cited by 605

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.SimplicialObject.Splitting.fromNondegComplex_f_assocproof · cited by 0