This is an invited survey article on higher gauge theory for the Encyclopedia of Mathematical
Physics, 2nd edition. In particular, we provide a lightning introduction to higher structures …

In this paper we introduce principal 2-bundles and show how they are classified by non-
abelian Čech cohomology. Moreover, we show that their gauge 2-groups can be described …

This is the second paper of a series dedicated to the study of Poisson structures of compact
types (PMCTs). In this paper, we focus on regular PMCTs, exhibiting a rich transverse …

For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie
groupoids, furnishing a differential graded-commutative Lie algebra equipped with an …

Let G be a finite group and Y a G-gerbe over an orbifold B. A disconnected orbifold Y ˆ and a
flat U (1)-gerbe c on Y ˆ is canonically constructed from Y. Motivated by a proposal in …

We introduce a notion of equivalence for singular foliations—understood as suitable families
of vector fields—that preserves their transverse geometry. Associated with every singular …

We construct a first-order local model for Poisson manifolds around a large class of Poisson
submanifolds and give conditions under which this model is a local normal form. The …

We use shifted symplectic geometry to construct the Moore-Tachikawa topological quantum
field theories (TQFTs) in a category of Hamiltonian schemes. Our new and overarching …

Stacky Lie groupoids are generalizations of Lie groupoids in which the “space of arrows” of
the groupoid is a differentiable stack. In this paper, we consider actions of stacky Lie …

In this paper, we introduce a notion of a principal 2-bundle over a Lie groupoid. For such
principal 2-bundles, we have produced a short exact sequence of VB-groupoids, namely …