Table of contents

• Articles

  • Algebraic databases - by [Patrick Schultz][schultz], [David I. Spivak][spivak], [Christina Vasilakopoulou][vasilakopoulou] and [Ryan Wisnesky][wisnesky]
  • Algebraic Model Management: A survey - by [Patrick Schultz][schultz], [David I. Spivak][spivak], and [Ryan Wisnesky][wisnesky]
  • Functorial data migration - by [David I. Spivak][spivak]
  • Categories of Containers - by [Michael Abbot][abbot], [Thorsten Altenkirch][altenkirch] and [Neil Ghani][ghani]
  • A categorical approach to open and interconnected dynamical systems - by [Brendan Fong][fong], [Paolo Rapisarda][rapisarda] and [Paweł Sobociński][sobocinski]
  • A semantical approach to equilibria and rationality - by [Dusko Pavlovic][pavlovic]
  • Compositional game theory - by [Jules Hedges][hedges], [Neil Ghani][ghani], [Viktor Winschel][winschel] and [Philipp Zahn][zahn]
  • The game semantics of game theory - by [Jules Hedges][hedges]
  • Free compact 2-categories - by Joachim Lambek and Anne Preller
  • Mathematical foundations for a compositional distributional model of meaning - by [Bob Coecke][coecke], [Mehrnoosh Sadrzadeh][sadrzadeh] and [Stephen Clark][clark]
  • The Frobenius anatomy of word meanings I: subject and object relative pronouns - by [Mehrnoosh Sadrzadeh][sadrzadeh], [Stephen Clark][clark] and [Bob Coecke][coecke]
  • Backprop as Functor: A compositional perspective on supervised learning - by [Brendan Fong][fong], [David I. Spivak][spivak] and [Rémy Tuyéras][tuyeras]
  • Compositional Deep Learning - by [Bruno Gavranović][gavranovic]
  • String diagrams for assembly planning - by [Jade Master][master], [Evan Patterson][patterson], Shahin Yousfi, Arquimedes Canedo
  • Generalized Petri Nets - by [Jade Master][master]
  • The Mathematical Specification of the Statebox Language - by [Fabrizio Genovese][genovese] and [Jelle Herold][herold]
  • A categorical approach to probability theory - by Michèle Giry
  • Causal inference by string diagram surgery - by [Bart Jacobs][jacobs], [Aleks Kissinger][kissinger] and [Fabio Zanasi][zanasi]
  • A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics - by [Tobias Fritz][fritz]

• Books

  • Category Theory for the Sciences - by [David I. Spivak][spivak]
  • Seven Sketches in Compositionality: An Invitation to Applied Category Theory - by [Brendan Fong][fong] and [David I. Spivak][spivak] (note also the [corresponding lecture series](#lectures)).
  • What is Applied Category Theory - by [Tai-Danae Bradley][bradley]
  • Category Theory for Programmers - by [Bartosz Milewski][milewski]

• Companies

  • Conexus - A start-up developing [CQL](https://www.categoricaldata.net/), 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](https://github.com/input-output-hk/plutus/tree/master/metatheory), [Coq](https://github.com/input-output-hk?language=coq) and [k-framework](https://testnet.iohkdev.io/iele/about/formal-verification/)
  • RChain - blockchain ecosystem it's foundational language - Rholang is implementation of [rho-calculus](http://rho.loria.fr/index.html) wih deep roots in [higher category theory](https://arxiv.org/abs/1504.04311) and [enriched Lawvere theories](https://arxiv.org/abs/1704.03080)

• Conferences

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

• Journals

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

• Lectures

  • Applied Category Theory @ MIT 2019 - by [Brendan Fong][fong] and [David I. Spivak][spivak]

• Meetups

  • Boston
  • Munich
  • New York
  • San Francisco Bay Area

• Software libraries

  • UniMath - categories formalized using univalent mathematics, in [Coq](https://coq.inria.fr/)

• Tools

  • Cartographer.id - a tool for string diagrammatic reasoning
  • Homotopy.io - a web-based proof assistant for finitely-presented globular n-categories
  • KdMonCat - a tool for drawing morphisms in monoidal categories