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Higher gauge theory
Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings)
From loop groups to 2-groups
We describe an interesting relation between Lie 2-algebras, the Kac– Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where
Higher Gauge Theory: 2-Connections on 2-Bundles
Connections and curvings on gerbes are beginning to play a vital role in differential geometry and mathematical physics -- first abelian gerbes, and more recently nonabelian gerbes. These concepts
Differential cohomology in a cohesive infinity-topos
We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we
Parallel Transport and Functors
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize
Connections on non-abelian Gerbes and their Holonomy
We introduce an axiomatic framework for the parallel transport of connections on gerbes. It incorporates parallel transport along curves and along surfaces, and is formulated in terms of gluing
L ∞ -Algebra Connections and Applications to String- and Chern-Simons n-Transport
We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L ∞-algebras and use it to study the obstruction theory of lifts through higher String-like extensions of
A Higher Stacky Perspective on Chern–Simons Theory
The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern–Simons-type gauge field theories. We explain in some detail how
Smooth functors vs. differential forms
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a