Researcher

Department of Distributed and Dependable Systems
Faculty of Mathematics and Physics
Charles University

Malostranské náměstí 25
118 00 Praha 1
Czech Republic

E-mail: corfield@d3s.mff.cuni.cz
Web: https://ncatlab.org/davidcorfield/
Office: 204, 2nd floor

Research

Through my academic career I worked as a philosopher of mathematics arguing that philosophy should engage with mathematics as it is actually practised, a case made in Towards a Philosophy of Real Mathematics (2003). I drew on the works of Lakatos, Kuhn and other philosophers of science to treat mathematics as a research tradition that grows through conceptual change. A central case study for over 30 years has been category theory and higher category theory.

In Modal Homotopy Type Theory (2020) I proposed that homotopy type theory and its modal extensions be taken as a new logic for philosophy, one that can handle structure, identity and modality better than first-order logic. Much of this work came out of his long collaboration on the n-Category Café blog with John Baez and Urs Schreiber, and out of the nLab, a wiki dedicated to higher category theory and its applications. I have further interests in inference that go back to my earlier work on Bayesianism and machine learning, and to my time at the University of Kent’s Centre for Reasoning.

Most recently I have been working on an ARIA-funded program: Safeguarded AI. My work has focused on the use of monad-comonad interactions to provide a framework for categorical systems theory. The target is a compositional theory of heterogeneous systems in which operational interfaces, stateful implementation, physical/probabilistic/resource effects, behaviour and certification are different faces of the same Sweedler structure. (Sweedler Runners for Systems)