- identity function
- isomorphism aka "an iso"
- category of rings
- enriched category
- intensional computation
- extensional computation
- partial order
category of rings
category of sets
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?"
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.