Project information
Higher Dimensional Aspects of First-Order Logic (HiDimAFOL)

Categorical logic is a syntax-independent approach to logic that treats logical connectives as algebraic operations. There is a well-developed literature on using 1-dimensional category theory to study first-order logic, the logic that forms the bedrock of most other areas of mathematics, but recently many new tools have been developed within higher dimensional category theory to study the higher order logics that appear in, for example, type theory. This project will explorethe less developed but nonetheless fruitful topic of higher dimensional categorical aspects of first order logic; namely, we will study those properties of first-order logic that only emerge in higher dimensions.
Specifically, we will explore three ways that 2-dimensional monads (2-monads) appear in
categorical logic. The notion of a monad is a key concept within (1-dimensional) category theory.
Although the development of monad theory has largely been guided by abstract algebra, monads can
nonetheless describe many mathematical objects that, on the surface, do not appear algebraic in nature, e.g. the ‘algebras’ for the ultrafilter monad are compact Hausdorff spaces