In
category theory in
mathematics a
family of generators (or
family of separators) of a
category ![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=110)
is a collection of objects, indexed by some set
I, such that for any two morphisms
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=1126)
in
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=110)
, if
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2842)
then there is some
i∈I and morphism , such that the compositions
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=4164)
. If the family consists of a single object
G, we say it is a
generator (or
separator).