Definition 89.21.7. Let $(U, R, s, t, c)$ be a groupoid in functors on a category $\mathcal{C}$. Let $\mathcal{C}'$ be a subcategory of $\mathcal{C}$. The *restriction $(U, R, s, t, c)|_{\mathcal{C}'}$ of $(U, R, s, t, c)$ to $\mathcal{C}'$* is the groupoid in functors on $\mathcal{C}'$ given by $(U|_{\mathcal{C}'}, R|_{\mathcal C'}, s|_{\mathcal{C}'}, t|_{\mathcal{C}'}, c|_{\mathcal{C}'})$.

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