Category Theory

Category Theory is a foundational representation of mathematics. It directly relates to how data and computation can be represented as functions or relations. Due to its generally applicable nature, it is so general that many mathematicians calls it Abstract nonsense.

The seminal paper, A General Theory of Natural Equivalence that defined the outline of Category Theory was written by Saunders MacLane and Samuel Eilenberg.

Category Theory Online Tutorials

For starters, the following video series would be great starting points for people who wants to know more about Category Theory.

To obtain an orientation of Category Theory, the following 3 part Category Theory introductory video series by John Peloquin can be finished in 30 minutes.

An ideal starting point for learning Category Theory is to know its nature of being a pure declarative style of reasoning, in contrast to the imperative style of reasoning. It can also be understood as a global vs. local approach to prescribe concepts. Bartosz Milewski has a great video on this subject, please see Video/Declarative vs Imperative Approach.

Local vs. Global Approach to define a function

Concepts\Programming Style	Imperative	Declarative
Mathematical Subject	Differential Equation	Category Theory
Scope	Local	Global
Physics	Classical	Quantum
Mechanics	Newtonian	Lagrangian

Richard Southwell

Richard Southwell has a youtube channel on many subjects about math, particularly having a long series on Category Theory.

Topos Institute

Topos Institute, founded by David Spivak and Brendan Fong, also has a youtube channel on Category Theory.

Topos institute publishes its lectures on Youtube, for example:

Toby St Clere Smithe has a talk at Topos Institute on: Compositional Active Inference: A “Process Theory” for Finding Right Abstractions

William Lawvere

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