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Conceptual Mathematics, Second Edition by Stephen H. Schanuel, F. William Lawvere

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ARTICLE I

image

Sets, maps, composition

A first example of a category

Before giving a precise definition of ‘category’, we should become familiar with one example, the category of finite sets and maps.

An image in this category is a finite set or collection. Here are some examples:

(the set of all students in the class) is one object,

(the set of all desks in the classroom) is another,

(the set of all the twenty-six letters in our alphabet) is another.

You are probably familiar with some notations for finite sets:

{John, Mary, Sam}

is a name for the set whose ...

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