Definition:Slice Category

Definition
Let $\mathbf C$ be a metacategory.

Let $C \in \mathbf C_0$ be an object of $\mathbf C$.

The slice category of $\mathbf C$ over $C$, denoted $\mathbf C / C$, is defined as follows:

By Slice Category is Category, this is indeed a category.

Also see

 * Coslice Category