The Stacks project

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. $\square$

Comments (1)

Comment #374 by Fan on

The equation does not seem right. and don't compose.

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  • 2 comment(s) on Section 12.14: Homotopy and the shift functor

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