Applied category theory
Applied category theory (ACT) is the name given to the recent renaissance in applying ideas from category theory to subjects outside of pure mathematics. In the 1980s and 1990s, category theory was widely applied in progamming language theory. The ongoing revival of ACT is broader in scope, using categories to model compositionality of processes in domains ranging from chemistry and quantum mechanics to electrical and software engineering. Monoidal categories are a major tool in this program.
Influential research programs in ACT include:
- Network theory, by John Baez and collaborators
- Operads for complex systems, by David Spivak and collaborators
- Categorical quantum mechanics , initiated by Samson Abramsky and Bob Coecke
For more resources, see the Awesome ACT repo.
Conferences
2021
2020
- ACT 2020 (nCat Cafe 1 ,2 )
- NIST ACT Workshop (Azimuth ), postponed indefinitely due to COVID-19
2019
- AMS Sectional Meeting, Special Session on ACT (nCat Cafe 1 ,2 , Azimuth 1 ,2 ,3 )
- At UC Riverside, organized by John Baez & Joe Moeller
- ACT 2019 (Azimuth , nCat Cafe )
- Live blogging by John Baez and Jules Hedges
2018
- ACT 2018 , the first Applied Category Theory Conference
- NIST ACT Workshop (YouTube , Azimuth 1 ,2 )
- Most slides and videos available
2017
- AMS Sectional Meeting, Special Session on ACT (nCat Cafe 1 ,2 ,3 )
- At UC Riverside, organized by John Baez
2016
- Fall 2016 Simons Workshop on Compositionality (Azimuth )
- Workshop on Semantic Spaces at the Intersection of NLP, Physics, and Cognitive Science (arxiv)
Seminars
- ACT seminar at UC Riverside, spring 2019 (Azimuth ), with videos online
- Baez: Mathematics in the 21st century (Azimuth )
- Lorand: Classification problems in symplectic linear algebra (Azimuth )
- Vasilakopoulou: Systems as wiring diagram algebras (Azimuth )
- Cicala: Social contagion modeled on random networks (Azimuth )
- Master: Backprop as functor (on work by Fong, Spivak and Tuyéras)
- Williams: The pi calculus: Towards global computing (Azimuth )
- Courser: Category theory for genetics (on work by Tuyéras)