What is a Category

A category “X” consists of some data that satisfy two properties:

1. **Identity **
   1. Each object “x” has an identity morphism

$$x\stackrel{{\text{id}}_x}{⟶}x$$ $${\text{id}}_y\circ f=f=f\circ {\text{id}}_x$$

2. Associativity (composition)

$$(h\circ g)\circ f=h\circ (g\circ f)$$

In category theory we are not interested in the individual elements of one category, instead we want to model and learn the relationships between categories.

Translating this for the “programming land”:

• Usually in programming land a category is a type, but we are not interested in the set of individual elements from this type… what we really want to understand is: how we can build relationships between different types?

https://www.math3ma.com/blog/what-is-a-category

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