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enter image description here As shown in the figure, $A_i $, $B_i$ and $C_i $on the left are all chain complexes, which make up 3 × 3 short exact sequences. Is the diagram on the right necessarily commutative?

($\partial $ is the homologous edge operator derived from snake lemma)

Arnaud D.
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GCauchy
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  • Welcome to Math.SE! Could you give some more background for this question, and indicate what you have tried so far? If it's a homework, there's not much point in giving you the full answer directly. – Hanno Nov 14 '19 at 13:30
  • Thanks, the background is from relative mayer-vietoris sequence in algebraic topology and the question is from Hatcher P152. @Hanno – GCauchy Nov 14 '19 at 14:02

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