Theorems · Definition · algebraic topology

CategoryTheory.SimplicialObject.Splitting.toNondegComplex

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {X : CategoryTheory.SimplicialObject C} →
      (s : X.Splitting) →
        [inst_1 : CategoryTheory.Preadditive C] → AlgebraicTopology.AlternatingFaceMapComplex.obj X ⟶ s.nondegComplex

Given a splitting s of a simplicial object X in a preadditive category, this is the split epimorphism from the alternating face map complex of X to the chain complex s.nondegComplex.

Defined in

Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Cited by

9 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive