This is the written version of a set of four lectures given at the CIB in Lausanne in April 2015.
The aim of these lectures was to present some of the mathematical-physical ideas …

We develop a new differential geometric structure using category theoretic tools that
provides a powerful framework for studying bundles over path spaces. We study a type of …

This is the first of a series of two technical papers devoted to the analysis of holonomy
invariants in strict higher gauge theory with end applications in higher Chern–Simons …

A crossed module constitutes a strict 2-groupoid G and a G-valued 2-cocycle on a manifold
defines a 2-bundle. A 2-connection on this 2-bundle is given by a Lie algebra g valued 1 …

A gauge theory is associated with a principal bundle endowed with a connection permitting
to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a …

A categorical principal bundle is a structure comprised of categories that is analogous to a
classical principal bundle; examples arise from geometric contexts involving bundles over …

We develop a theory of twisted actions of categorical groups using a notion of semidirect
product of categories. We work through numerous examples to demonstrate the power of …

We construct a cycle in higher Hochschild homology associated to the two-dimensional
torus which represents 2-holonomy of a nonabelian gerbe in the same way as the ordinary …

Holonomy invariants in strict higher gauge theory have been studied in depth aiming to
applications to higher Chern–Simons theory. For a flat 2–connection, the holonomy of …

Categorical bundles provide a natural framework for gauge theories involving multiple
gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality …