Category Theory Illustrated - Categories

In this chapter we will continue with set theory, and at the same time we will start exploring categories and talking about why they are important. In the previous chapter, we needed a way to make a set that is a composite of other sets that we already have. For example, when we discussed mathematical functions, we couldn’t define + and - functions, because we only knew about functions that take one argument. When we talked about programming, we talked about the primitive types, Char and Number, and we mentioned that most of the types are composite types. So how do we construct those? The simplest composite type, of the sets B, which contains b’s and the set Y, which contains y’s is the product of B and Y. The product is the set of ordered pairs of b’s and y’s. It is denoted B x Y and it comes equipped with two functions for retrieving the b and the y from each (b, y). The product is denoted B x Y, and it comes equipped with two functions for retrieving the b and the y from each (b, y)

In this chapter we will continue with set theory, and at the same time we will start exploring categories and talking about why they are important. In the previous chapter, we needed a way to make a set that is a composite of other sets that we already have. For example, when we discussed mathematical functions, we couldn’t define + and - functions, because we only knew about functions that take one argument. When we talked about programming, we talked about the primitive types, Char and Number, and we mentioned that most of the types are composite types. So how do we construct those? The simp