Theorems · Definition · algebraic topology

CategoryTheory.SimplicialObject.Splitting.nondegComplex

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {X : CategoryTheory.SimplicialObject C} → X.Splitting → [inst_1 : CategoryTheory.Preadditive C] → ChainComplex C ℕ

If s is a splitting of a simplicial object X in a preadditive category, s.nondegComplex is a chain complex which is given in degree n by the nondegenerate n-simplices of X. This chain complex should be thought as the normalized chain complex of X because of the isomorphism toKaroubiNondegComplexIsoN₁.

Defined in

Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject

Cited by

31 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive