The whole point of category theory is to study fundamental general abstract patterns and phenomena that (re-)appear throughout mathematics. Hence applications of theorems of category theory are ubiquituous in mathematics and in subjects with a mathematical basis, such as physics and computer science. Often this goes without saying.
In the introduction to Bradley 18 it says:
… ideas and results from category theory have found applications in computer science and quantum physics (not to mention pure mathematics itself), but these are not the only applications to which the word applied in applied category theory is being applied…
category theory has found applications in a wide range of disciplines outside of pure mathematics—even beyond the closely related fields of computer science and quantum physics. These disciplines include chemistry, neuroscience, systems biology, natural language processing, causality, network theory, dynamical systems, and database theory to name a few. And what do they all have in common? … In other words, the techniques, tools, and ideas of category theory are being used to identify recurring themes across these various disciplines with the purpose of making them a little more formal.
Tai-Danae Bradley, What is applied category theory?, arXiv:1809.05923
Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory, arXiv:1803.05316.
John Baez ran a series of lectures based on this book:
lectures on chapter 1
lectures on chapter 2
David Spivak, Category theory for the sciences. MIT Press, 2014.
Brandon Coya?, Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective, arXiv:1805.08290
John Baez and Brendan Fong, A Compositional Framework for Passive Linear Networks, arXiv:1504.05625
Blake Pollard?, Open Markov processes: A compositional perspective on non-equilibrium steady states in biology, arXiv:1601.00711
Brendan Fong, The Algebra of Open and Interconnected Systems, arXiv:arXiv:1609.05382
John Baez and Blake Pollard?, A Compositional Framework for Reaction Networks, arXiv:1704.02051
John C. Baez, Brendan Fong and Blake Pollard?, A Compositional Framework for Markov Processes, arXiv:1508.06448
Jules Hedges and Martha Lewis?, Towards Functorial Language-Games, arXiv:1807.07828
Last revised on March 13, 2023 at 11:59:39. See the history of this page for a list of all contributions to it.