Applied category theory is an

academic discipline An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy ...

in which methods from

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

are used to study other fields including but not limited to

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

(in particular

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

natural language processing Natural language processing (NLP) is an interdisciplinary subfield of linguistics, computer science, and artificial intelligence concerned with the interactions between computers and human language, in particular how to program computers to pro ...

control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

and

causality Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...

. The application of category theory in these domains can take different forms. In some cases the formalization of the domain into the language of category theory is the goal, the idea here being that this would elucidate the important structure and properties of the domain. In other cases the formalization is used to leverage the power of abstraction in order to prove new results about the field.

List of applied category theorists

Samson Abramsky Samson Abramsky (born 12 March 1953) is Professor of Computer Science at University College London. He was previously the Christopher Strachey Professor of Computing at the University of Oxford, from 2000 to 2021. He has made contributions to t ...

John C. Baez John Carlos Baez (; born June 12, 1961) is an American mathematical physics, mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California, Riverside, California. He has worked o ...

* Bob Coecke *

Joachim Lambek Joachim "Jim" Lambek (5 December 1922 – 23 June 2014) was a German-born Canadian mathematician. He was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his PhD degree in 1950 with Hans Zassenhaus as ...

Valeria de Paiva Valeria Correa Vaz de Paiva is a Brazilian mathematician, logician, and computer scientist. Her work includes research on logical approaches to computation, especially using category theory, knowledge representation and natural language semanti ...

* Gordon Plotkin * Dana Scott *

David Spivak David Isaac Spivak is an American mathematician and senior scientist at the Topos Institute. He has worked on applications of category theory, in particular ologs and operadic compositionality of dynamical systems. He authored and coauthored th ...

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

TallCat
a research group at

Tallinn University of Technology Established in 1918, Tallinn University of Technology (TalTech; et, Tallinna Tehnikaülikool) is the only technical university in Estonia. TalTech, in the capital city of Tallinn, is a university for engineering, business, public administratio ...

Topos Institute

Cybercat Institute
Software:
DisCoPy
a

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

toolkit for computing with

string diagrams String diagrams are a formal graphical language for representing morphisms in monoidal categories, or more generally 2-cells in 2-categories. They are a prominent tool in applied category theory. When interpreted in the monoidal category of vector ...

CatLab.jl
a framework for applied category theory in the

Julia language Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic programmin ...

References

Category theory {{categorytheory-stub

List of applied category theorists

See also

External links

References