Algebraic Topology Series: Unlocking the Power of Category Theory 🧠

Playlist: https://www.youtube.com/playlist?list=PLOROtRhtegr7DmeMyFxfKxsljAVsAn_X4

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.
Learn more about math at Andrews University: https://www.andrews.edu/cas/math/
In this course we are following Hatcher, Algebraic Topology: https://pi.math.cornell.edu/~hatcher/AT/AT.pdf