"Categories for the Working Hacker" by Philip Wadler: good technical intro that hits the sweet spot of notational choice, topic selection and relevance to thining categorically.

• What is Applied Category Theory?: Tai-Danae Bradley's paper. Start here.

• John Baez's summary

• Seven Sketches in Compositionality: Spivak and Fong's work.

• Topology: A Categorical Approach: A graduate-level textbook that presents basic topology from the perspective of category theory.

• The Dao of Functional Programming: by Bartosz Milewski.

• An Introduction to Category Theory: by Robin Truax.

• Category Theory in Context: by Emily Rhiel.

• Applied Category Theory Youtube: Videos of 2019 MIT Applied Category Theory by Brendan Fong and David Spivak. In this course, we will give seven sketches on real-world applications of category theory.

• Programming with Categories : By Brendan Fong, David Spivak and Bartosz Milewski.

  • Summary: In this course we explain how category theory—a branch of mathematics known for its ability to organize the key abstractions that structure much of the mathematical universe—has become useful for writing elegant and maintainable code. In particular, we'll use examples from the Haskell programming language to motivate category-theoretic constructs, and then explain these constructs from a more abstract and inclusive viewpoint. Hands-on programming exercises will be used to demonstrate categorical ideas like "the universal property of products" in working Haskell code.

• Abstract Algebra by Benedict Gross at Harvard.

  • Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields. In these free videotaped lectures, Professor Gross presents an array of algebraic concepts.

• "Categories for the Working Hacker" by Philip Wadler: good technical intro that hits the sweet spot of notational choice, topic selection and relevance to thining categorically.

• A Crash Course in Category Theory at F(by) 2017: Intro with emphasis on Types: Void, Unit, Product, Coproduct (sum). The monoidal categories for Product, Coproduct and Natural Transformation (category where objects are functors) are presented.

• A Crash Course in Category Theory at ScalaIO France 2017: by Bartosz Milewski. More detail than the F-by version. This one has a great explanation of Yoneda embedding which is a special case of the the Yoneda lemma.

• Group Theory by Steven Roman

• Category Theory by Steven Roman

• Category Theory for Programmers: Bartosz Milewski's lecture series.

• The Casters' Category Theory Videos: Eugenia Cheng et. al's original series.

• Tai-Danae Bradley Modeling Language with Tensor Networks

  • Abstract: Natural language has both a compositional and a statistical structure. These structures emerge when expressions in language combine to form longer expressions, and where the validity of an expression is captured by the statistics in the language. One model for this is a monoidal functor from a category of grammar to an appropriate semantics category. Another modeling choice is to let statistics serve as a proxy for grammar, taking inspiration from quantum probability theory. This talk features the latter. I’ll share an elementary passage from classical probability to quantum probability and use it to describe a tensor network model for language.

• AFOSR_Proposal--Agent_Interaction_II--2018: Spivak's proposal suggesting the application of category theory on a broad look at machine learning.

  • We seek a mathematical framework for specifying various aspects of an autonomous agent and its interactions with other agents, including humans. Just like linear algebra offers tools and ideas that can be used in a wide range of applications—machine learning, statistics, differential equations, graphics processing, and so on—we need a mathematical language and toolset that can be used to conceptualize and interrelate the sorts of concerns that arise when considering autonomous agents and their interaction, in all its forms. In this proposal, we lay out a vision for using category theory to manage the interaction of various sorts of agents (including human agents), as well as the sorts of planning and learning that makes autonomy possible