Lemma 14.22.5. Let \mathcal{A} be an abelian category. For any simplicial object V of \mathcal{A} we have
V = \mathop{\mathrm{colim}}\nolimits _ n i_{n!}\text{sk}_ n V
where all the transition maps are injections.
Proof. This is true simply because each V_ m is equal to (i_{n!}\text{sk}_ n V)_ m as soon as n \geq m. See also Lemma 14.21.10 for the transition maps. \square
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