# An invitation to geometric higher categories (external link)

Fast and mathematically self-contained introduction to basic ideas in geometric higher category theory, written up as an article for the n-Category Café.

Researcher at Vaticle.

- United Kingdom
- Vaticle
- Oxford Math
- Oxford CS
- Cambridge Math
- ETH Physics
- GitHub

first published

Fast and mathematically self-contained introduction to basic ideas in geometric higher category theory, written up as an article for the n-Category Café.

Comments first published

Pattern matching is an ubiquitous tool in theoretical computer science and type-theoretical mathematics, as well as the formalization of formal languages themselves. We briefly review its role in these subjects, giving examples along the way. We then motivate a deeper connection between pattern matching and higher-dimensional geometry, and suggest how geometric type theory, while not a real type theory yet, tries to provide a general formal framework in which mathematics can be built from higher-dimensional patterns. → read note

Comments first published

This short note takes a birds-eye perspective on motivations for working as a researcher in mathematics and physics (which are first and foremost motivations personal to me, but I think they may be shared with many others). I briefly round up some (glimmers of) potentially interesting projects that I find fascinating. The note is written on the occasion on moving on to other endeavors. → read note

Comments first published

Mazur manifolds are intimately related to homology spheres, and are part of the puzzling world of 4-manifolds. Here we construct the simplest example of a Mazur manifold as a tangle diagram. → read note

Comments first published

We allow ourselves to speculate a bit about how the 1-dimensional logical constructs that one frequently encounters in practical approaches to mathematical foundations may in fact emerge from a set of “more fundamental” principles of compositionality in higher-dimensional logic. → read note