Related papers: Parallel 2-transport and 2-group torsors
The Langlands functoriality conjecture, as reformulated in the "beyond endoscopy" program, predicts comparisons between the (stable) trace formulas of different groups $G_1, G_2$ for every morphism ${^LG}_1\to {^LG}_2$ between their…
Properties of (most general) non-commutative torsors or A-B torsors are analysed. Starting with pre-torsors it is shown that they are equivalent to a certain class of Galois extensions of algebras by corings. It is shown that a class of…
We generalize the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. Given a multifusion 2-category, potentially with some additional levels of…
Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following…
In this paper, we continue the study of the category of functors Fquad, associated to F_2-vector spaces equipped with a nondegenerate quadratic form, initiated in two previous papers of the author. We define a filtration of the standard…
In this paper we construct classifying localic categories and groupoids for various bundles equipped with logical structure. When these bundles are local homeomorphisms, we recover the localic groupoids that classify geometric theories,…
Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that…
Let $G$ be a connected reductive group, with connected center, and $X$ a smooth complete curve, both defined over an algebraically closed field of characteristic zero. Let $\operatorname{Bun}_G$ denote the stack of $G$-bundles on $X$. In…
In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring $\cR$, we prove…
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract…
We introduce a candidate for the inner hom for $Dbl^{st}_{lx}$, the category of strict double categories and lax double functors, and characterize a lax double functor into it obtaining a lax double quasi-functor. The latter consists of a…
We prove that the category of abelian gerbes with connection over a smooth manifold is equivalent to a certain category of principal bundles over the free loop space. These bundles are equipped with a connection and with a "fusion" product…
A tangent category is a category with an endofunctor, called the tangent bundle functor, which is equipped with various natural transformations that capture essential properties of the classical tangent bundle of smooth manifolds. In this…
We generalize Quillen's Theorem A to diagrams of lax 2-functors which commute up to transformation. It follows from a special case of this result that 2-categories are models for homotopy types.
We set up a framework of 2-Hilbert bundles, which allows to rigorously define the "stringor bundle", a higher differential geometric object anticipated by Stolz and Teichner in an unpublished preprint about 20 years ago. Our framework…
In the previous article 'A Mackey-functor theoretic interpretation of biset functors', we have constructed the 2-category $\mathbb{S}$ of finite sets with variable finite group actions, in which bicoproducts and bipullbacks exist. As shown…
A new category $\mathfrak{dp}$, called of dynamical patterns addressing a primitive, nongeometrical concept of dynamics, is defined and employed to construct a $2-$category $2-\mathfrak{dp}$, where the irreducible plurality of species of…
In this paper, we introduce the classification of equivariant principal bundles over the 2-sphere. Isotropy representations provide tools for understanding the classification of equivariant principal bundles. We consider a…
In this article, we construct a 2-shaded rigid ${\rm C}^*$ multitensor category with canonical unitary dual functor directly from a standard $\lambda$-lattice. We use the notions of traceless Markov towers and lattices to define the notion…
In this short note we give an elementary proof of the fact that connections and their geometric parallel-transport counterpart are equivalent notions.