I am interested in all sorts of mathematics, but I mostly write about topology: in particular, how to apply category theory to homotopy theory.

Some public research

Here is a development page for a paper I'm writing about 2-dimensional pasting diagrams.


It's possible to see what I have on the ArXiv.

Concrete Categories in Homotopy Type Theory
Some comments about how to do categories in univalent foundations
Algebraic theories, span diagrams and commutative monoids in homotopy theory
The first half of my PhD thesis, plus a few neat extra results. Under revision.
Algebraic theories and (∞,1)-categories
My PhD thesis at the University of Sheffield (2010).

Preprints in preparation

Feel free to contact me if you would like a working copy of these.

  1. Rings and semirings in homotopy theory via algebraic theories
  2. Cofibre sequences, Frobenius objects and duality
  3. Abstract polytopes in homotopy theory