We describe an approach to the verified implementation of transformations on functional programs that exploits the higher-order representation of syntax. In this approach, transformations are specified using the logic of hereditary Harrop formulas (HOHH). On the one hand, these specifications serve directly as implementations, being programs in the language λProlog. On the other hand, they can ...

The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional TQFTs are to be described as n-category representations. First we describe a ‘suspension’ operation on ncategories, a...

A bstract In four-dimensional axion electrodynamics, a Chern-Simons coupling of the form ?F ^ F leads to higher-group global symmetry between background gauge fields. At same time, such mixing Weak Gravity Conjectures for and field, so that charged excitations Conjecture-satisfying string will also satisfy Conjecture field. this paper, we argue these symmetries phenomenon are related one anothe...

There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and outlined for weak ncategories. The categorical aspects concern the development of descent theory in low dimensions in order to provide a template for a theory in...

We fill a gap in the literature regarding ‘transport of structure’ for (n+2)-angulated, n-exact, n-abelian and n-exangulated categories appearing (classical higher) homological algebra. As an application our main results, we show that skeleton one these kinds inherits same structure canonical way, up to equivalence. In particular, it follows weak (n+2)-angulated category is fact what call stron...