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LICENSE add MIT license Oct 2, 2019 fix order of database section papers Nov 11, 2019

Awesome Applied Category Theory

A curated list of Applied Category Theory resources.

Table of contents


Relevant articles applying category theory to various fields.


Data types

Dynamical systems

Game theory


Machine learning


Petri nets

Probability and statistics


Books on applied category theory.


Companies applying category theory.

Heavily using ACT

  • Conexus - A start-up developing CQL, a generalization of SQL to data migration and integration that contains an automated theorem prover to rule out most semantic errors at compile time.
  • Statebox - building a formally verified process language using robust mathematical principles to prevent errors, allow compositionality and ensure termination

Interested in ACT research


  • ACT - Applied Category Theory Conference
  • Statebox Summit - An yearly gathering of category theorists and functional programmers
  • SYCO - Symposium on Compositional Structures


Academic journals on applied category theory.

  • Compositionality - open-access journal for research using compositional ideas, most notably of a category-theoretic origin, in any discipline


Video recordings of lecture series on applied category theory.


Software libraries

Libraries to actually encode category theory in software.


Useful tools for applied category theory.

  • - a tool for string diagrammatic reasoning
  • Catlab.jl - an experimental framework for applied category theory
  • - a web-based proof assistant for finitely-presented globular n-categories
  • KdMonCat - a tool for drawing morphisms in monoidal categories
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