Categorical algebra

Okay kiddo, let's first talk about categories. Categories are a way of organizing things, like toys or animals. In categorical algebra, we use categories to study mathematical objects like numbers, functions, and shapes.

Now, imagine a category called "Sets". In this category, objects are sets of things, like a set of toys or a set of animals. And the arrows (or morphisms) between objects are functions that link one set to another.

Categorical algebra studies properties that are common to all categories, like how objects and arrows can be combined to form new objects and arrows. These operations are called compositions.

For example, if we have a function from set A to set B, and another function from set B to set C, we can compose them to get a new function from set A to set C. This is called functional composition.

Categorical algebra also deals with universal properties. These are properties that hold for all objects in a category. For example, the product of two sets in the "Sets" category is a set that contains all possible pairs of elements, one from each set.

In summary, categorical algebra is a branch of mathematics that studies the properties of categories and the ways in which objects and arrows within them can be combined. It helps us understand mathematical structures in a more abstract and general way.