The Stacks project

Example 18.37.3. Let $G$ be a group. Consider the site $\mathcal{T}_ G$ and its point $p$, see Sites, Example 7.33.7. Let $R$ be a ring with a $G$-action which corresponds to a sheaf of rings $\mathcal{O}$ on $\mathcal{T}_ G$. Then $\mathcal{O}_ p = R$ where we forget the $G$-action. In this case $p^{-1}p_*M = \text{Map}(G, M)$ and $I(M) = \{ f : G \to M \mid f(1_ G) = 0\} $ and $M \to \text{Map}(G, M)$ assigns to $m \in M$ the constant function with value $m$.