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The world runs on information, but what is it? Information seems to have something in common with mathematics: there are certain rules necessary to keep it consistent and useful. We don't just mean information in Claud Shannon's sense---meaningless data passing over a noisy channel---to us, information is meaningful, and that is important. We want to know the operations one can perform that respect meaningful information. As the mathematician Daniel Kan said, "Information is inherently a combinatorial affair."

But what is the right mathematics for handling information? Information lies on a spectrum, from chaotic to organized. Chaotic information, for which a pattern needs to be found, should be handled by probabilistic or machine-learning methods. But once something usable and known has been extracted from the chaos, it should be organized algebraically, i.e., according to principled transformations that preserve its structure and integrity. For this one should use category theory, the mathematics of structure.

Category theory was designed to build bridges between different conceptual landscapes. It has been very successful in doing so for the field of mathematics, and we have reason to believe it will do so for informatics as well. It does not unify, as if to create one world-view to rule them all; instead it connects, allowing different disciplines to remain distinct, but interoperable by way of a rigorous, flexible system of translation.


EASIK: Entity-Attribute Sketch Implementation Kit

FQL/AQL: A Functorial/Algebraic Query Language

Matriarch: A Language for Materials Architecture

Ologs: Ontology Logs

Operadics: Mathematics for Modularity

Get Involved

Members of the community have made many contributions to our projects, including: We welcome collaborators: The broader applied category theory community has a site here.