What's the name of this category

We can usually build new categories from old ones, as example we have the slice $\mathfrak C/A$ and coslice categories $A/\mathfrak C$ of $\mathfrak C$ with an object $A$. I'm reading this book and I'm looking for the name of this new from the category $\mathfrak C$ with its standard symbol:

Thanks

• Isn't it isomorphic to the category $C_{A\times B}$? – Alex Nelson Apr 22 '14 at 20:42
• @AlexNelson What I know $A\times B$ is the final object of $C_{A,B}$ – user42912 Apr 22 '14 at 20:49
• @AlexNelson but my goal is know if this kind of category has a special name as slice and coslice categories. – user42912 Apr 22 '14 at 20:50
• @AlexNelson and know if the $C_{A,B}$ is indeed the standard symbol of this kind of category. – user42912 Apr 22 '14 at 20:51

It is the category of cones over the diagram $\{0,1\} \to \mathsf C : 0 \mapsto A, 1 \mapsto B$. I don't think there is a standard notation for it.
• if you call your functor $F$, then this category is called $Cone(F)$. You can find this notation in Awodey , for example. – magma Apr 22 '14 at 23:12