Lemma. We have ∂n−1∘∂n=0\partial_{n-1} \circ \partial_n = 0 [URFG]

2026-10-04 · Lîm Tsú-thuàn

The composition CnΔ(X)→∂nCn−1Δ(X)→∂n−1Cn−2Δ(X)C^\Delta_n(X) \xrightarrow{\partial_n} C^\Delta_{n-1}(X) \xrightarrow{\partial_{n-1}} C^\Delta_{n-2}(X)DefinitionBoundary homomorphism (also known as differential)2026-10-04 · Lîm Tsú-thuàn is the zero map.