Publications

1. Double clubs, Cahiers de Topologie et Géométrie Différentielle Catégoriques 47 (2006), no. 4, 261–317.
2. Polycategories via pseudo-distributive laws, Advances in Mathematics 218 (2008), no. 3, 781–827.
3. The low-dimensional structures formed by tricategories (with Nick Gurski), Mathematical Proceedings of the Cambridge Philosophical Society, in press.
4. Understanding the small object argument, Applied Categorical Structures, in press.
5. The identity type weak factorisation system (with Nicola Gambino), Theoretical Computer Science 409 (2008), no. 3, 94–109
6. On the strength of dependent products in the type theory of Martin-Löf, Annals of Pure and Applied Logic, in press.
7. A homotopy-theoretic universal property of Leinster's operad for weak ω-categories, Mathematical Proceedings of the Cambridge Philosophical Society, in press.
8. Two-dimensional models of type theory, Mathematical Structures in Computer Science, in press.
9. Homomorphisms of higher categories, Submitted.
10. Types are weak ω-groupoids (with Benno van den Berg), Submitted.
11. Ionads: a generalisation of the notion of topological space.

Teaching

1. Examples Sheet 1 PS PDF
2. Examples Sheet 2 PS PDF
3. Examples Sheet 3 PS PDF
4. Examples Sheet 4 PS PDF

Other material

1. Making weak maps compose strictly, Presentation at Category Theory 2008, Calais, 2008–06–27.
2. Two-dimensional locally cartesian closed categories, Presentation at Workshop on Categorical and Homotopical Structures in Proof Theory, Barcelona, 2008–02–16.
3. The theory of glueing things on, Presentation at Category Theory 2007, Carvoeiro, 2007–06–20.
4. Cofibrantly generated natural weak factorisation systems, Uppsala University Department of Mathematics Technical Report 2007:13.
5. When pseudo comes for free, Presentation at PSSL 85, Nice, 2007–03–24.
6. Polycategories, PhD Thesis, 2006.
7. Three investigations into linear logic, First year PhD report, 2005.

Contact Information