I am working on applications of category theory. I work in the private sector and do my research as a hobby. I am developing a categorical approach to science where the concept of data is embedded in a natural way and is well understood. I have done work to address how theories relate to experiments. I have recently been very influenced by the work of David Spivak.
I like to think about the causal structure approach to quantum gravity. I have looked for Bimonads on Set as analogies to Frobenius monads on Symmetric Monoidal Categories like Hilb. I have been looking at the adjunctions into the Giry monad, and just factorizations of Monads in general. I am also revisiting the idea of generalizing the Giry Monad, for instance setting in a suitable category of categories, or creating a (co)monad that captures probability measures. I have found the work of Brendan Fong interesting and was trying to show that Causal theories are internal categories and are also Bimonads (in the case of Sets). Recently, I have been fascinated by the use of Monads to capture data structures, in the form of containers like Lists, and how this is related to fundamental physics.