Category theory: abstracting mathematical construction (essay)

In real life, and in particular, in mathematics, there are entities and actions.

We can consider types of entities.

For example, let us consider two such types $X$ and $Y$, where $X={\text{apples}}$ and $Y={\text{pie}}$.

There is a specific apple sitting in my fridge,

There's an action of baking apple pie

too broad

Definition of a category

Definition. A category ${\mathcal {C}}$ consists of the following data:

1. A class