Category Theory - Lecture 6 Part 2
Channel: An Antipodal Algebraic Topologist
Date: 2019-07-09

In this video we show that a unit/counit pair satisfying the triangle identities is equivalent to an adjunction. We then see a different equivalent notion of adjunction. We talk about some key adjoint pairs in algebraic topology, and also take a moment to define the homology of a chain complex and, by composing with some other functors, the homology of a topological space. Then we see that under some conditions taking the limit of a functor is an adjoint functor. Finally I state (but do not prove) that Right Adjoints Preserve Limits.

Unfortunately some of the board is cut off between about 7:30 and 14:15, the important information is still visible.