A functor $F\colon \mathcal{C}\to \mathcal{D}$ is injective on objects if the action on objects
\[ F\colon \operatorname {\mathrm{Obj}}(\mathcal{C})\to \operatorname {\mathrm{Obj}}(\mathcal{D}) \]
of $F$ is injective.
-
(b)
The functor $F$ is an isocofibration in $\mathsf{Cats}_{\mathsf{2}}$.
11.8.1 Injective on Objects Functors
Let $\mathcal{C}$ and $\mathcal{D}$ be categories.
Let $F\colon \mathcal{C}\to \mathcal{D}$ be a functor.
Proof of Proposition 11.8.1.1.2.
Item 1: Characterisations
Omitted.
