In the category , a function is defined as a set of ordered pairs that satisfies the following:

- If and
- If ,
- Then .

In other words, is itself a set! Specifically, it is a subset of the *Cartesian Product* of and where we presumably were taking our original elements. (, and .) So, .

- The
*domain*of is the set of all objects , such that for some object . - The
*range*is the set of all objects such that for some object .

If is the domain of , and is a set that (at least) contains the range of (that is, ), then we say that * is a function from into *. We can write this as: .

*Now go lift something heavy,*

Nick Horton