Difference between revisions of "Category Theory"
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Category Theory is a foundational representation of mathematics. It directly relates to how data and computation can be represented as [[function]]s or [[relation]]s. Due to its generally applicable nature, it is so general that many mathematicians calls it [[abstract nonsense]]. | Category Theory is a foundational representation of mathematics. It directly relates to how data and computation can be represented as [[function]]s or [[relation]]s. 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<ref>Samuel Eilenberg, Saunders MacLane, General Theory of Natural Equivalences, Transactions of the American Mathematical Society | The seminal paper, A General Theory of Natural Equivalence<ref>Samuel Eilenberg, Saunders MacLane, General Theory of Natural Equivalences, Transactions of the American Mathematical Society | ||
Revision as of 03:54, 9 August 2021
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[1] 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.
| Concepts\Programming Style | Imperative | Declarative |
|---|---|---|
| Mathematical Semantics | Algorithmic Sequence | Category Theory |
| Scopes | Local | Global |
| Scientific Doctrines | Classical Physics | Quantum Physics |
| Scientific Doctrines | Action-Reaction | Stationary Action Principle |
| Analytical Modeling | Newtonian Mechanics | Lagrangian Mechanics |
| Infrastructure Automation | Ansible | Terraform |
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
{{#ev:youtube|https://www.youtube.com/watch?v=ZYGyEPXu8as%7C%7C%7C%7C%7C}}
References
- ↑ Samuel Eilenberg, Saunders MacLane, General Theory of Natural Equivalences, Transactions of the American Mathematical Society Vol. 58, No. 2 (Sep., 1945), pp. 231-294, American Mathematical Society, https://www.jstor.org/stable/1990284?seq=1