Definition:Coslice Category

Definition
Let $\mathbf C$ be a metacategory.

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

The coslice category of $\mathbf C$ under $C$, denoted $C / \mathbf C$, is defined as follows:

By Coslice 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}, "C";"X" **@{-} ?>*@{>} ?*!/^.6em/{f}, "C";"X2" **@{-} ?>*@{>} ?<>(.6)*!/_1em/{f'}, \end{xy}$

Also see

 * Slice Category