Geometry of figures and algebra of functions
The notion of category embraces at least three related sorts of mathematical environments:
(a) an abstract theory of some notion (such as ‘preorder’ or ‘group’ or ‘dynamical evolution’);
(b) a background (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 ...