How does one split up a long exact sequence into short exact sequences?
Say you have some longs exact sequences of modules $ 0\longrightarrow M_1\stackrel{\phi_1}{\longrightarrow}M_2\stackrel{\phi_2}{\longrightarrow}M_3\stackrel{\phi_3}{\longrightarrow}M_4\stackrel{\phi_4}{\longrightarrow}\cdots $ I've read it's possible to split this into short exact sequences. What exactly does that mean? Would it be written as short exact sequences, one appended to another like 0\longrightarrow N_1\longrightarrow M_1\longrightarrow N'_1\longrightarrow 0\longrightarrow N_2\longrightarrow M_2\longrightarrow N'_2\longrightarrow 0 \longrightarrow\cdots? If so, how does this work? Merci.