Theorems · Theorem · category theory

ChainComplex.alternatingConst_exactAt

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasZeroObject C] (X : C) (n : ℕ),
  n ≠ 0 → HomologicalComplex.ExactAt (ChainComplex.alternatingConst.obj X) n

The n-th homology of the alternating constant complex is X for n ≠ 0.

Defined in

Mathlib.Algebra.Homology.AlternatingConst

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObject