Every category $\mathrm{𝒞︀}$ is a bicategory $\text{𝖫𝖣}(\mathrm{𝒞︀})$ with only identity 2-cells. Its 0-cells are the objects of $\mathrm{𝒞︀}$, and the hom-category $\text{𝖫𝖣}(\mathrm{𝒞︀})(𝑥,𝑦)$ is the discrete category on the set $\mathrm{𝒞︀}(𝑥,𝑦)$: a 2-cell $𝑓\Rightarrow 𝑔$ is a proof that $𝑓=𝑔$. Composition and identities are those of $\mathrm{𝒞︀}$; the unitors and associator are the unit and associativity laws of $\mathrm{𝒞︀}$. Since the homs of $\mathrm{𝒞︀}$ are sets, any two parallel 2-cells are equal, so the triangle and pentagon hold trivially.

A functor $𝐹:\mathrm{𝒞︀}\to \mathrm{𝒟︀}$ gives a pseudofunctor $\text{𝖫𝖣}(𝐹):\text{𝖫𝖣}(\mathrm{𝒞︀})\to \text{𝖫𝖣}(\mathrm{𝒟︀})$, whose comparison 2-cells are the functor laws of $𝐹$.

The locally discrete bicategory is how ordinary indexed categories enter bicategorical language: a prestack on $\text{𝖫𝖣}(\mathrm{𝒞︀})$ is a pseudofunctor ${\mathrm{𝒞︀}}^{\text{op}}\to \text{𝖢𝖠𝖳}$, and its Grothendieck construction is a displayed category over $\mathrm{𝒞︀}$.