Overcategory
Category
| context | C … category |
| context | T∈C |
| definiendum | C/T |
| definition | ObC/T:= all arrows f, such that there is an object S∈C, such that f:C[S,T] |
| definition | C/T[f,g]:= all arrows h, such that h∘g=f |
Elaboration
Given a (target) object T in any category C, the over category C/T has objects all arrows into T, and arrows all forwardings of their domains (there is one for each commutative triangle).
Reference
nLab: Overcategory
Subset of
