A short exact sequence of chain complexes 0 → A → B → C → 0 induces a natural long exact sequence in homology, with connecting map ∂: H_n(C) → H_{n−1}(A) given by the zig-zag construction: lift a cycle c ∈ C_n to b ∈ B_n, take db ∈…
A short exact sequence of chain complexes 0 → A → B → C → 0 induces a natural long exact sequence in homology, with connecting map ∂: H_n(C) → H_{n−1}(A) given by the zig-zag construction: lift a cycle c ∈ C_n to b ∈ B_n, take db ∈…