In this easy introduction to higher gauge theory, we describe parallel transport for particles
and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a …

" The book is extremely pleasant to read, with masterfully crafted exercises and examples
that create a beautiful and unique thread of presentation leading the reader safely into the …

The language of∞-categories provides an insightful new way of expressing many results in
higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …

This research monograph is divided into three parts. Broadly speaking, Part I belongs to the
realm of category theory, while Parts II and III pertain to algebraic combinatorics, although …

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it
became clear that underlying these diagrams is a powerful analogy between quantum …

We prove the conjecture that any Grothendieck $(\infty, 1) $-topos can be presented by a
Quillen model category that interprets homotopy type theory with strict univalent universes …

In some bicategories, the 1-cells aremorphisms' between the 0-cells, such as functors
between categories, but in others they areobjects' over the 0-cells, such as bimodules …

Dimension three is an important test-bed for hypotheses in higher category theory and
occupies something of a unique position in the categorical landscape. At the heart of matters …

We prove that the rank of the cohomology of a closed symplectic manifold with coefficients in
a field of characteristic $ p $ is smaller than the number of periodic orbits of any non …

We develop some aspects of the theory of derivators, pointed derivators and stable
derivators. Stable derivators are shown to canonically take values in triangulated categories …