Lemma 12.14.6. Notation and assumptions as in Lemma 12.14.4 above. Suppose $\{ s'_ n : C_ n \to B_ n\}$ is a second choice of splittings. Write $s'_ n = s_ n + i_ n \circ h_ n$ for some unique morphisms $h_ n : C_ n \to A_ n$. The family of maps $\{ h_ n : C_ n \to A[-1]_{n + 1}\}$ is a homotopy between the associated morphisms $\delta (s), \delta (s') : C_\bullet \to A[-1]_\bullet$.

Proof. Omitted. $\square$

Comment #374 by Fan on

The equation $s_n' = s_n + \pi_n \circ h_n$ does not seem right. $h_n: C_n \to A_n$ and $\pi_n: B_n \to A_n$ don't compose.

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