category theory

# concepts

• identity function
• isomorphism aka “an iso”
• domain
• co-domain
• target
• arrows
• associativity
• category of rings
• enriched category
• intensional computation
• extensional computation
• partial order

# cutting room floor

Category theory is the mathematics of mathematics. Okay, so then what is Mathematics? It’s the logical study of how logical things work. Thus category theory is the logical study of how logical things work.

Category makes logical connections between things

A family tree is an example of category theory. It provides a way of representing relationships.

# The principle of Sameness

``````8 + 1 = 1 + 8
2 x 5 = 5 x 2
(8+5) +5 = 8 + (5+5)
``````

The concept of invertibility - “if I go over here can I go back?”

# Universal Properties

If you freeze water, it goes back to water. If you freeze an egg and

Whole categories can be isomorphic if the arrows look the same. The first row is isomorphic because the arrows go the same way, the bottom row isn’t isomorphic.