The Language of Categories | Category Theory and Why We Care 1.1

By first outlining a mathematically rigorous definition of a category, we can embark on a fascinating journey through category theory with examples from mathematics, computer science and logic.

This video establishes a good grounding for any keen mathematicians, formally trained or not, and aims to make dealing with the complicated structure of a category feel more natural. With plenty of examples to challenge your understanding, we'll venture into the incredibly abstract world of category theory.

― Corrections ―

12:04 - This should be: It is sunny ∧ (It is sunny ⇒ Bob wears a hat). The and operator ∧ typically has higher precedence than implication, so brackets must be used to ensure this proposition has the meaning I intended it to have.

― Timestamps ―

0:00 - Intro
0:58 - Definition
6:02 - Set
9:46 - Category of Proofs
16:00 - Functional Programming
18:34 - Outro

― Credits ―

All animation and voiceover created by Eyesomorphic.
Background music: 'Raindrops on glass', composed by Caleb Peppiatt.

― Further Reading ―

Category Theory, by Steve Awodey (Book)