[Inquiry] Re: Category Theory

[Jon Awbrey]

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CAT.  Note 4

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| Introduction (cont.)
|
| The construction "cartesian product" is called a "functor"
| because it applies suitably to sets 'and' to the functions
| between them;  two functions k : X -> X' and h : Y -> Y'
| have a function k x h as their cartesian product:
|
| k x h : X x Y -> Y x Y',  <x, y> ~> <k x, h y>.
|
| Observe also that the one-point set 1 = {0} serves as an identity
| under the operation "cartesian product", in view of the bijections:
|
|        !q!       !r!
| 1 x X -----> X <----- X x 1
|
| given by !q!<0, x> = x, !r!<x, 0> = x.
|
| Mac Lane, 'Cat Work Math', p. 2.
|
| Saunders Mac Lane,
|'Categories for the Working Mathematician',
| 2nd edition, Springer, New York, NY, 1997.

Nota Bene.  I am having to change the names of some of Mac Lane's maps,
due to his use of letters like "l" and the Greek lambda !l! that do not
asciify without risk of confusion with the number 1 and the identity !1!.

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