Category theory

A category is a mathematical structure consisting of objects and morphisms. If there are objects and morphisms, and the following two conditions are met, it is a category:

• Identity morphism

• Associativity

First Condition (Identity morphism)

create is a monoid because it has a single object that satisfies the Identity morphism.

• create -> create

• keyname -> keyname

• css-property -> css-property

$A \circ A = A$

$A \oplus I = A$

Where the first expresses idempotency and the second expresses identity.

Second Condition (Associativity)

The law of associativity states that the result is the same regardless of the order in which the expressions are calculated.

Given [A, B, C]:

• (A + B) + C
• A + (B + C)

result in the same result, thus satisfying the compositional condition of the associative law.

$(A \oplus B) \oplus C = A \oplus (B \oplus C)$

Composition of Monoids

When this is assigned to styling,

[styles.A, styles.B, styles.C]

Then, the monoid create is a category with objects in composition.

Ultimately, it always converges to a single result.
This is proof that a styling system closed to static analysis satisfies the axioms of category theory.

$parse(A \oplus B \oplus C) \to \text{"classA classB classC"}$