Commit 2025-08-06 10:52 fc48d275
View on Github →feat(Algebra/Homology/AlternatingConst): generalize to any appropriate complex shape and pair of maps (#27361)
Given an object X : C
and endomorphisms φ, ψ : X ⟶ X
such that φ ∘ ψ = ψ ∘ φ = 0
, this PR defines the periodic chain and cochain complexes ... ⟶ X --φ--> X --ψ--> X --φ--> X --ψ--> 0
and 0 ⟶ X --ψ--> X --φ--> X --ψ--> X --φ--> ...
(or more generally for any complex shape c
on ℕ
where c.Rel i j
implies i
and j
have different parity).
We calculate the homology of these periodic complexes.
This generalizes some of the current content of the file, which works for the chain complex where ψ = 0
and φ = Id
.