mkavand / awesome-applied-category-theory

ACT community resources

Awesome applied category theory

A curated list of awesome Applied Category Theory resources.

Table of contents

• Awesome ACT
  • Articles
    • Databases
    • Data types
    • Dynamical systems
    • Game theory
    • Machine learning
    • Petri nets
  • Books
  • Companies
  • Conferences
  • Journals
  • Software libraries
  • Tools

Articles

Relevant articles applying category theory to various fields.

Databases

• Algebraic databases - by Patrick Schultz, David I. Spivak, Christina Vasilakopoulou and Ryan Wisnesky
• Functorial data migration - by David I. Spivak

Data types

• Categories of containers - by Michael Abbot, Thorsten Altenkirch and Neil Ghani

Dynamical systems

• A categorical approach to open and interconnected dynamical systems - by Brendan Fong, Paolo Rapisarda and Paweł Sobociński

Game theory

• The game semantics of game theory - by Jules Hedges

Machine learning

• Backprop as Functor: A compositional perspective on supervised learning - by Brendan Fong, David I. Spivak and Rémy Tuyéras
• Compositional Deep Learning - by Bruno Gavranović

Petri nets

• Generalized Petri Nets - by [Jade Master]
• The Mathematical Specification of the Statebox Language - by Fabrizio Genovese and Jelle Herold

Books

Books on applied category theory.

• Category theory for the sciences - by David I. Spivak
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory - by Brendan Fong and David I. Spivak
• What is Applied Category Theory - by Tai-Danae Bradley

Companies

Companies applying category theory.

• Conexus - developing CQL, a tool for data migrations
• Statebox - building a formally verified process language using robust mathematical principles to prevent errors, allow compositionality and ensure termination

Conferences

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

Journals

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

Software libraries

Libraries to actually encode category theory in software.

• copumpkin/categories - categories parametrized by morphism equality, in Agda
• idris-ct - a formally verified category theory library written in Idris

Tools

Useful tools for applied category theory.

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