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Conceptual Mathematics, Second Edition by Stephen H. Schanuel, F. William Lawvere

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APPENDIX I

images

Geometry of figures and algebra of functions

1. Functors

The notion of category embraces at least three related sorts of mathematical environments:

(a)    an abstract theory images of some notion (such as ‘preorder’ or ‘group’ or ‘dynamical evolution’);

(b)    a background images (such as smooth spaces) in which that notion might be realized;

(c)    the concrete totality of realizations of in .

The example (a) reflects the observation that the substitutions ...

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