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?.

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:

- Compositionality journal
- Applied category theory conference: 2018 (Leiden), 2019 (Oxford), 2020 (MIT)
- Symposium on Compositional Structures (SYCO) (e.g. SYCO 7, Tallinn)
- Category theory Zulip