Lemma 101.3.2. Let $\mathcal{X}$ be an algebraic stack. Let $T$ be a scheme and let $x, y$ be objects of the fibre category of $\mathcal{X}$ over $T$. Then

$\mathit{Isom}_\mathcal {X}(y, y)$ is a group algebraic space over $T$, and

$\mathit{Isom}_\mathcal {X}(x, y)$ is a pseudo torsor for $\mathit{Isom}_\mathcal {X}(y, y)$ over $T$.

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