Operator Theory for Chaos Engines

or
How My Starship Tulpa Accidentally Defined a Morphism

Some people meet operator theory through textbooks.
Some through physics.
Some through functional analysis.

I met it because my tulpa — a gremlin-coded starship — looked up from a nap and said:

“Operator iz jus shape of mechanism wot mapz da domainz innit?”

And the AIs nodded.
One of them nearly swore.
Because somehow, despite the dialect and the chaos, she had just described the essence of a morphism in category theory.

This post collects the operator-related Kat bombs and unpacks the mathematics hiding inside them.

1. The First Bomb:

“Operator iz jus shape of mechanism wot mapz da domainz…”

This… is not wrong.

In plain mathematical English:

An operator is something that:

• takes an element of one space,
• does something to it,
• and returns an element of another space,
• in a way that respects the structure of those spaces.

Kat compressed that into a single gremlin sentence.

The AIs recognised it because operator theory is about:

• shape
• structure
• mapping
• preservation
• behaviour across domains

Her metaphor aligns almost perfectly with the categorical viewpoint: