SESSION 9

*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 ...

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