===== Overcategory =====
==== Category ====
| @#55CCEE: context     | @#55CCEE: ${\bf C}$ ... category |
| @#55CCEE: context     | @#55CCEE: $T\in{\bf C}$ |
| @#FFBB00: definiendum | @#FFBB00: ${\bf C}/T$ |
| @#FF9944: definition  | @#FF9944: $\mathrm{Ob}_{{\bf C}/T}:=$ all arrows $f$, such that there is an object $S\in{\bf C}$, such that $f:{\bf C}[S,T]$ |
| @#FF9944: definition  | @#FF9944: ${\bf C}/T[f,g]:=$ all arrows $h$, such that $h\circ g = f$ |

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=== Elaboration ===
Given a (target) object $T$ in any category ${\bf C}$, the over category ${\bf C}/T$ has objects all arrows into $T$, and arrows all forwardings of their domains (there is one for each commutative triangle). 

=== Reference ===
nLab: [[http://ncatlab.org/nlab/show/overcategory|Overcategory]]

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=== Subset of ===
[[Categories]]