A category is a formal thing, which means that it is literally composed of "objects" and "arrows," and that these names, and the entities themselves, mean nothing. We can think of a category as a set of objects, and for each ordered pair of (not necessarily distinct) objects a set of arrows from the first to the second. Additionally, there is a binary operator on arrows, composition, which gives an arrow X->Z for each pair of arrows X->Y, Y->Z.
Categories are useful because they allow a lot of interpretations, or in other words many things can be represented as categories. The category of sets, for example, has an object for each set and an arrow for each function. The category of rings uses rings and ring homomorphisms, etc. There is also a category of categories, which contains an object for each category (although some are barred to avoid paradoxes), and an arrow for each functor between categories. This allows us to work with categories under functors as we would any other object. Marshall On Mon, Apr 2, 2012 at 4:20 PM, Raul Miller <rauldmil...@gmail.com> wrote: > I am already noticing errors in my last post. > > For example, please replace 'domain bit' with 'domain but' > > 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
