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.

The morphisms can be displayed using a commutative diagram as follows:


 * $\begin{xy}

<-3em,0em>*+{X} = "X", <3em,0em>*+{X'} = "X2", <0em,-4em>*+{C} = "C",

"X";"X2" **@{-} ?>*@{>} ?*!/_1em/{a}, "X";"C" **@{-} ?>*@{>} ?<>(.3)*!/^1em/{f}, "X2";"C" **@{-} ?>*@{>} ?<>(.3)*!/_1em/{f'}, \end{xy}$

Also see

 * Coslice Category