Theorems · Theorem · algebraic topology

CategoryTheory.SimplicialObject.Splitting.comp_PInfty_eq_zero_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X : CategoryTheory.SimplicialObject C} (s : X.Splitting)
  [inst_1 : CategoryTheory.Preadditive C] {Z : C} {n : ℕ} (f : Z ⟶ X.obj (Opposite.op { len := n })),
  CategoryTheory.CategoryStruct.comp f (AlgebraicTopology.DoldKan.PInfty.f n) = 0 ↔
    CategoryTheory.CategoryStruct.comp f
        (s.πSummand (CategoryTheory.SimplicialObject.Splitting.IndexSet.id (Opposite.op { len := n }))) =
      0

Defined in

Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Cited by

2 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive