Definition 2.2.8.24. Let $\operatorname{\mathcal{C}}$ be a $2$-category. We say that $\operatorname{\mathcal{C}}$ is a $2$-groupoid if every $1$-morphism in $\operatorname{\mathcal{C}}$ is an isomorphism and every $2$-morphism of $\operatorname{\mathcal{C}}$ is an isomorphism.
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