1. Category

Category is a simple concept. In fact, most things in category theory can be embarrassingly simple to explain.

Category requires only 2 things. Objects and morphisms. Whatever a thing is, if you can map it into a bunch of objects and morphisms with rules in 1.2 Properties of Composition, you have a category.

An object can be whatever. A morphism can change an object to another object.

1.1 Morphism as Functions

We can reimagine morphism as functions instead. Like functions, morphism are composable. Meaning if there exists $a\to b$ and $b\to c$ , then we can use both to construct $a\to c$ .

1.2 Properties of Composition

1. Composition is associative, meaning: $h◦(g◦f)=(h◦g)◦f=h◦g◦f$
2. For every object, there exist identity function where $f◦id=f$

Next: 2. Types and Functions