Remark 89.21.3. Let $(U, R, s, t, c)$ be a groupoid in functors on a category $\mathcal{C}$. There are unique morphisms $e : U \to R$ and $i : R \to R$ such that for every object $T$ of $\mathcal{C}$, $e: U(T) \to R(T)$ sends $x \in U(T)$ to the identity morphism on $x$ and $i: R(T) \to R(T)$ sends $a \in U(T)$ to the inverse of $a$ in the groupoid category $(U(T), R(T), s, t, c)$. We will sometimes refer to $s$, $t$, $c$, $e$, and $i$ as “source”, “target”, “composition”, “identity”, and “inverse”.

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