Tai-Danae Bradley is a mathematician who received her Ph.D. in mathematics from the CUNY Graduate Center. She was formerly at Alphabet and is now at Sandbox AQ, a startup focused on combining machine learning and quantum physics. Tai-Danae is a visiting research professor of mathematics at The Master’s University and the executive director of the Math3ma Institute, where she hosts her popular blog on category theory. She is also a co-author of the textbook Topology: A Categorical Approach that presents basic topology from the modern perspective of category theory.In this episode, we provide a compressed crash course in category theory. We provide definitions and plenty of basic examples for all the basic notions: objects, morphisms, categories, functors, natural transformations. We also discuss the first basic result in category theory which is the Yoneda Lemma. We conclude with a discussion of how Tai-Danae has used category-theoretic methods in her work on language modeling, in particular, in how the passing from syntax to semantics can be realized through category-theoretic notions.Patreon: https://www.patreon.com/timothynguyenOriginally published on July 20, 2022 on YouTube: https://youtu.be/Gz8W1r90olcTimestamps:Further Reading:Tai-Danae's Blog: https://www.math3ma.com/categoriesTai-Danae Bradley. "What is applied category theory?" https://arxiv.org/pdf/1809.05923.pdfTai-Danae Bradley, John Terilla, Yiannis Vlassopoulos. "An enriched category theory of language: from syntax to semantics." https://arxiv.org/pdf/2106.07890.pdf