SESSION 24

*Uniqueness of products and definition of sum*

In the last session we gave two exercises: one concerning the uniqueness of products and the other the definition of sum. One way of thinking about product and sum is that they combine two objects to get another object. In this session we will see that any product or sum also allows you to combine maps to get a new map. (Of course we already have one way of combining maps to get another map, namely *composition* of maps.)

**1. The terminal object as an identity for multiplication**

Let’s start with an example to see how the uniqueness of products is useful. We saw that in the category of sets the number of elements of the product of two sets is precisely the product of the respective numbers ...

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