Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer science, physics (in particular quantum mechanics), natural language processing, control theory, probability theory and causality. 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 or to develop new algorithms about the field.
List of applied category theorists
Samson Abramsky John C. Baez Bob Coecke Joachim Lambek Valeria de Paiva Gordon Plotkin Dana Scott David Spivak
See also
Categorical quantum mechanics ZX-calculus DisCoCat Petri net Univalent foundations String diagrams
External links Journals:
Compositionality
Conferences:
Applied category theory Symposium on Compositional Structures (SYCO)
Books:
Picturing Quantum Processes Categories for Quantum Theory An Invitation to Applied Category Theory (preprint) Category Theory for the Sciences (preprint)
Institutes:
the Quantum Group at the University of Oxford TallCat, a research group at Tallinn University of Technology Topos Institute Cybercat Institute UDBMS, a research group at University of Helsinki Software:
DisCoPy, a Python toolkit for computing with string diagrams CatLab.jl, a framework for applied category theory in the Julia language CQL, a query language based on Kan extensions
Companies:
Conexus AI, a data integration company Symbolica, a machine learning company
Mascots:
Gremlin-Morgoth
References