applied category theory

Applied category theory (ACT) refers to a diverse community of researchers attempting to apply ideas from category theory? to various fields outside of mathematics. A non-exhaustive list of subjects to which category theory has been applied includes physics?, chemistry?, biology?, engineering?, computer science?, economics? and linguistics?.

Major subfields

Much work within ACT shares a common foundation: the use of monoidal categories? to compositionally? describe some class of open systems?. This includes:

  • categorical quantum mechanics?
  • categorical compositional distributional semantics? (DisCoCat) in linguistics
  • decorated cospans? and related constructions
  • compositional game theory?

Other subfields that do not fall into this general pattern include:

  • topological data analysis?
  • Category theory in functional programming?

Events and community