Category Theory For Beginners: Linear Algebra

We start by discussing the new visual approach to linear algebra based on Props. We show how wiring diagrams can be used to easily think about matrix algebra. Next we discuss the category of vector spaces. We discuss various categorical features of the category of vector spaces, like limits, colimits, biproducts, kernels, cokernels, tensor products and so on. And we finish by reconnecting this general approach with matrix algebra. Resources: https://graphicallinearalgebra.net/ Seven Sketches in Compositionality: An Invitation to Applied Category Theory Brendan Fong, David I Spivak https://arxiv.org/abs/1803.05316 Frederic Latremoliere The Category of Vector Spaces (YouTube playlist) https://www.youtube.com/watch?v=J2ohPzXHpzQ&list=PLFJf6jNakNILaJMxmC9hB2FxkzFMRoyf1