Learning Category theory should be as easy as A -> B -> C.

A is a category

A -> B is an arrow, often called a morphism, but we're not going to be all highfalutin about this.

Think of A -> B like a function which takes type A, and returns type B. After all, types can be seen as a specific kind of category, and functions can be seen as a specific kind of arrow. It can be helpful to pretend say A is an int, and B here is a string, maybe C is a float but really they can be any type as long as they are not the same.

The rest of it is just stuff you already know. To qualify as a category it must be associative aka (A -> B) -> C == A -> (B -> C) and it must be possible to make arrows that don't change the category such as A -> A, B -> B and C -> C. You can see how if f = A -> B; and g = B -> C we can compose f, and g to make an arrow from A -> C.

Any time you have things (categories), and verbs (arrows) which meet associativity, and identity (which is usually the verb of doing nothing) you can do category theory to it.