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:


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

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    $\begingroup$ if you call your functor $F$, then this category is called $Cone(F)$. You can find this notation in Awodey , for example. $\endgroup$ – magma Apr 22 '14 at 23:12
  • $\begingroup$ Is there any special name to this category? $\endgroup$ – user42912 Apr 23 '14 at 4:38

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