Mathematics — Graph Theory · exact-sequences-algebra
Problem
Show that a commutative diagram
⋯→Cn+1↘An↙Bn→Cn↘An−1↙Bn−1→⋯
with the two sequences across the top and bottom exact, gives rise to an exact sequence ⋯→En+1→Bn→Cn⊕Dn→En→Bn−1→⋯ where the maps are obtained from those in the previous diagram in the obvious way, except that Bn→Cn⊕Dn has a minus sign in one coordinate.