Hi, my name is Matteo Capucci.

I'm a PhD student at the University of Strathclyde, in the MSP group. My area of research is applied category theory, though I'm more on the 'pure applied' side than the 'applied applied'. What I mean is that I like to apply categorical (and topos-theoretical) structural reasoning to different areas of math, and hopefully of applied math.

In my MSc work I tried to frame stochastic calculus as an externalization of a simpler theory in a topos of 'stochastic sets'. My original presentation of such topos was through a localic tripos, but now I'm in the process of reworking everything in terms of sheaves, hence to present the same topos with a site.

Now I'm setting off to a new project, which is 'topos-theoretical systems theory'. The idea is to represent systems as sites and observations of said systems as sheaves. Cohomology would give us information about generative effects, proposition in the internal language should express behavioural constraints, and Morita equivalence should be 'bisimilarity', i.e. behavioural equivalence. Here's my point of contact with prof. Caramello's work on bridges, which could find some interesting applications in systems theory if the above checks out.

The bottom line is: I'll probably be asking a lot of questions here!