A gentle introduction to the study of category theory and abstract algebra, done from the ground-up by exploring the mathematical weapon of abstraction.
This video aims to give an overview of the fundamental tool at the forefront of pure mathematical research: abstraction. By seeing this tool in various contexts, and how it allows us to encounter category theory in a natural and intuitive manner, we'll see how beautiful the abstract can really be.
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.
To fully utilise the exciting category theory we've learnt so far, we need a way to abstract definitions from a specific category and then be able to apply them in any category we want. The solution to this is universal construction.
This video will explore the process of universal construction and see it used in practice, which will further expose some elegant relationships between categories that we've seen before. Taking examples from mathematical proofs, functional programming and beyond, this is the next major step into abstraction that our category theory journey takes us.