"The category of sets" means the category whose objects are sets and whose arrows are functions. I suppose it's more precise to call it "the category of sets and functions," but no one does that.
Since each arrow has a start and end point, the identity arrow for one element can't be the same as the identity for another, because they have different endpoints. Marshall On Mon, Apr 2, 2012 at 9:12 PM, Raul Miller <rauldmil...@gmail.com> wrote: > On Mon, Apr 2, 2012 at 6:30 PM, Marshall Lochbaum <mwlochb...@gmail.com> > wrote: > > A category is the collection of arrows AND objects. The objects alone do > > not define the category, so there can be many categories with the same > set > > of objects. > > That was my original impression. > > If this is the case, talking about "The category of > sets" or "The category of rings" does not mean anything, > since we do not know what arrows are in this category. > > > There is an additional requirement that there be an "identity" arrow from > > each object to itself. This and composition make arrows act enough like > > functions to be useful. > > Does this mean one arrow which is an identity for all objects? > > Or does this mean one arrow for each object which is an identity arrow? > > Or is it sufficient to have an arrow which is an identity arrow > without regard for the cardinality of such arrows? > > Thanks, > > -- > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
