The Stacks project

Definition 4.31.1. A final object of a $(2, 1)$-category $\mathcal{C}$ is an object $x$ such that

1. for every $y \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$ there is a morphism $y \to x$, and

2. every two morphisms $y \to x$ are isomorphic by a unique 2-morphism.