A curated list of Applied Category Theory resources.
Relevant articles applying category theory to various fields.
- Algebraic databases - by Patrick Schultz, David I. Spivak, Christina Vasilakopoulou and Ryan Wisnesky
- Algebraic Model Management: A survey - by Patrick Schultz, David I. Spivak, and Ryan Wisnesky
- Functorial data migration - by David I. Spivak
- A categorical approach to open and interconnected dynamical systems - by Brendan Fong, Paolo Rapisarda and Paweł Sobociński
- A semantical approach to equilibria and rationality - by Dusko Pavlovic
- Compositional game theory - by Jules Hedges, Neil Ghani, Viktor Winschel and Philipp Zahn
- The game semantics of game theory - by Jules Hedges
- Free compact 2-categories - by Joachim Lambek and Anne Preller
- Mathematical foundations for a compositional distributional model of meaning - by Bob Coecke, Mehrnoosh Sadrzadeh and Stephen Clark
- The Frobenius anatomy of word meanings I: subject and object relative pronouns - by Mehrnoosh Sadrzadeh, Stephen Clark and Bob Coecke
- Backprop as Functor: A compositional perspective on supervised learning - by Brendan Fong, David I. Spivak and Rémy Tuyéras
- Compositional Deep Learning - by Bruno Gavranović
- String diagrams for assembly planning - by Jade Master, Evan Patterson, Shahin Yousfi, Arquimedes Canedo
- Generalized Petri Nets - by Jade Master
- The Mathematical Specification of the Statebox Language - by Fabrizio Genovese and Jelle Herold
- A categorical approach to probability theory - by Michèle Giry
- Causal inference by string diagram surgery - by Bart Jacobs, Aleks Kissinger and Fabio Zanasi
- A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics - by Tobias Fritz
Books on applied category theory.
- Category Theory for Programmers - by Bartosz Milewski
- 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 (note also the corresponding lecture series).
- What is Applied Category Theory - by Tai-Danae Bradley
Companies applying category theory.
- 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
- IOHK - builds cryptocurrencies and blockchain solutions, based on peer reviewed papers; formally verified specifications in Agda, Coq and k-framework
- RChain - blockchain ecosystem it's foundational language - Rholang is implementation of rho-calculus wih deep roots in higher category theory and enriched Lawvere theories
- 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.
- Applied Category Theory @ MIT 2019, series of lectures based on the "Seven Sketches" book - by Brendan Fong and David I. Spivak
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
- UniMath - categories formalized using univalent mathematics, in Coq
Useful tools for applied category theory.
- Cartographer.id - a tool for string diagrammatic reasoning
- 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
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