Retracts and idempotents
1. Retracts and comparisons
We have seen that a reasonable notion of ‘same size’ is given by isomorphism: (read ‘A is isomorphic to B’) means that there is at least one invertible map (isomorphism) from A to B. For finite sets, tells us precisely that A and B have the same number of points, or maps from a singleton set 1. (In other categories, we’ll see that it tells us much more.) What is a good way to express that A is ‘at most as big as’ B? There are several answers, and we’ll discuss two of them. The first ...