Obvious Lemma: 0 → C n(A) −→ Cn(X) −→ Cn(X, A) → 0 is a short exact sequence. Thus this short exact sequence induces
![D. Zack Garza on Twitter: "And now the beautiful machinery of homological algebra kicks in for us: by the Snake Lemma, any short exact sequence of chain complexes will induce a *long* D. Zack Garza on Twitter: "And now the beautiful machinery of homological algebra kicks in for us: by the Snake Lemma, any short exact sequence of chain complexes will induce a *long*](https://pbs.twimg.com/media/EZc_ypcWsAAIhQZ.png)
D. Zack Garza on Twitter: "And now the beautiful machinery of homological algebra kicks in for us: by the Snake Lemma, any short exact sequence of chain complexes will induce a *long*
![algebraic topology - Long exact sequence for a triple follows from long exact sequence for a pair? - Mathematics Stack Exchange algebraic topology - Long exact sequence for a triple follows from long exact sequence for a pair? - Mathematics Stack Exchange](https://i.stack.imgur.com/IUs4G.png)