Remark 59.23.2. Let $G$ be an abstract group. On any of the sites $(\mathit{Sch}/S)_\tau $ or $S_\tau $ of Section 59.20 the sheafification $\underline{G}$ of the constant presheaf associated to $G$ in the *Zariski topology* of the site already gives

This Zariski sheaf is representable by the group scheme $G_ S$ according to Groupoids, Example 39.5.6. By Lemma 59.15.8 any representable presheaf satisfies the sheaf condition for the $\tau $-topology as well, and hence we conclude that the Zariski sheafification $\underline{G}$ above is also the $\tau $-sheafification.

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