Subsection 9.8.3 (016P): Bijective on Objects Functors

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Let $\mathcal{C}$ and $\mathcal{D}$ be categories.

A functor $F\colon \mathcal{C}\to \mathcal{D}$ is bijective on objects¹ if the action on objects

\[ F\colon \text{Obj}\webleft (\mathcal{C}\webright )\to \text{Obj}\webleft (\mathcal{D}\webright ) \]

of $F$ is a bijection.

¹Further Terminology: Also called a bo functor.

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