Algebraic Topology 19: Category Theory

What is category theory? In this lecture we introduce categories, which includes objects, morphismisms between those objects, and compositions of those morphisms. We give several examples. We then define functors between categories, showing that homology and the fundamental group are both examples of functors. And finally we introduce the idea of a natural transformation, discussing how the boundary map is a natural transformation between the homology functors H_n and H_{n-1}.

Presented by Anthony Bosman, PhD.

[ikechukwumichael]

Thank you very much.I have been checking your YouTube channel almost daily for the next uploads.

[nickrr]

I've watched a few introductory videos on category theory and this is by far the clearest! Thanks.

[markborz]

The example with the kontravariant functor with dual space is very clear and insightful!

[hyperduality]

Covariant is dual to contravariant -- vectors or Functors (dual spaces)!
Categories (form, syntax) are dual to sets (substance, semantics) -- category theory.
Syntax is dual to semantics -- languages or communication, information is dual.
If mathematics is a language then it is dual.
"Always two there are" -- Yoda.
The Yoneda lemma is duality!

[arhi-]

soos stole mysterious mushrooms from waddles 😭😭🙏🏻🙏🏻

[bennoarchimboldi]

This man is the michael penn of algebraic topology 😂😂