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 identity type weak factorisation system (with Nicola Gambino), Theoretical Computer Science 409 (2008), no. 3, pages 94–109
  4. The low-dimensional structures formed by tricategories (with Nick Gurski), Mathematical Proceedings of the Cambridge Philosophical Society 146 (2009), no. 3, pages 551–589.
  5. Understanding the small object argument, Applied Categorical Structures 17 (2009), no. 3, pages 247–285.
  6. On the strength of dependent products in the type theory of Martin-Löf, Annals of Pure and Applied Logic 160 (2009), no.1, pages 1–12.
  7. A homotopy-theoretic universal property of Leinster's operad for weak ω-categories, Mathematical Proceedings of the Cambridge Philosophical Society 147 (2009), no. 3, pages 615–628.
  8. Two-dimensional models of type theory, Mathematical Structures in Computer Science 19 (2009), no. 4, pages 687–736.
  9. Variable binding, symmetric monoidal closed theories, and bigraphs (with Tom Hirschowitz and Aurélien Pardon), Lecture Notes in Computer Science 5710 (2009), pages 321–337.
  10. Homomorphisms of higher categories, Advances in Mathematics 224 (2010), no. 6, pages 2269–2311.
  11. Types are weak ω-groupoids (with Benno van den Berg), Proceedings of the London Mathematical Society 102 (2011), no. 2, pages 370–394.
  12. Topological and simplicial models of identity types (with Benno van den Berg), Transactions of the ACM on Computational Logic 13 (2012), no. 1, pages 3:1–3:44.
  13. Lex colimits (with Stephen Lack), Journal of Pure and Applied Algebra 216 (2012), no. 6, pages 1372–1396.
  14. Grothendieck quasitoposes (with Stephen Lack), Journal of Algebra 355 (2012), no. 1, pages 111–127.
  15. Remarks on exactness notions pertaining to pushouts, Theory and Applications of Categories 27 (2012), no. 1, pages 2–9.
  16. An abstract view on syntax with sharing, Journal of Logic and Computation 22 (2012), no. 6, pages 1427–1452.
  17. Ionads, Journal of Pure and Applied Algebra 216 (2012), no. 8–9, pages 1734–1747.
  18. On the axioms for adhesive and quasiadhesive categories (with Stephen Lack), Theory and Application of Categories 27 (2012), no. 3, pages 27–46.
  19. On semiflexible, flexible and pie algebras (with John Bourke), Journal of Pure and Applied Algebra 217 (2012), no. 2, pages 293–321.
  20. A characterisation of algebraic exactness, Journal of Pure and Applied Algebra 217 (2013), no. 8, pages 1421--1426.
  21. Revisiting the categorical interpretation of dependent type theory (with Pierre-Louis Curién and Martin Hofmann), to appear in Theoretical Computer Science.
  22. Restriction categories as enriched categories (with Robin Cockett), submitted.
  23. Enriched categories as a free cocompletion (with Michael Shulman), submitted.
  24. Two-dimensional regularity and exactness (with John Bourke), submitted.

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

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Last edited 2013–04–14