Related papers: Dualities in the complicial model of $\infty$-cate…
In this paper we classify endofunctors on the simplex category, and we identify those that induce weak equivalence preserving functors on the category of simplicial sets.
The "linear dual" of a cocomplete linear category $\mathcal C$ is the category of all cocontinuous linear functors $\mathcal C \to \mathrm{Vect}$. We study the questions of when a cocomplete linear category is reflexive (equivalent to its…
I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two…
The results of this thesis allows one to replace calculations in tricategories with equivalent calculations in Gray categories (aka semistrict tricategories). In particular the rewriting calculus for Gray categories as used for example by…
We analyze the resurgence properties of finite-dimensional exponential integrals which are prototypes for partition functions in quantum field theories. In these simple examples, we demonstrate that perturbation theory, even at arbitrarily…
New self-dualities involving two index tensors are derived. These new self-dualities are used to build various duality cascades. Both vector like and chiral cascades are presented. Aside from ending in confinement, these duality cascades…
Using the strong relation between coactions of a discrete group G on C*-algebras and Fell bundles over G, we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the…
We discuss the relationship between target space modular invariance and discrete gauge symmetries in four-dimensional orbifold-like strings. First we derive the modular transformation properties of various string vertex operators of the…
A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions $f\colon X\to \overline{L^0}$ is established where $(X,Y,\langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\overline{L^0}$ is the set of…
The goal of this paper is to provide the last equivalence needed in order to identify all known models for $(\infty,2)$-categories. We do this by showing that Verity's model of saturated $2$-trivial complicial sets is equivalent to Lurie's…
We prove a comparison result between two duality statements - Takai duality, which is implemented by the crossed product functor $- \rtimes G: KK^{G} \to KK^{\hat G}$ on equivariant Kasparov categories; and Treumann duality, which asserts…
We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…
The reflexive completion of a category consists of the Set-valued functors on it that are canonically isomorphic to their double conjugate. After reviewing both this construction and Isbell conjugacy itself, we give new examples and revisit…
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations on a category A in the category of categories over A are studied; in particular, the reflections and the coreflections of the latter in the…
In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for…
In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories. We describe a method to construct model structures on…
We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group $G$ and when restricted to either a Frobenius kernel $G_r$ or a finite Chevalley group…
We generalize the construction of tensor categories of endomorphisms of a type III factor $M$ associated with a $G$-kernel, from the case of a discrete group $G$ to that of a compact second countable group. Our approach is based on the…
We construct a category $\OrdFor$ as an arboreal extension of $\Delta_{\mathrm{epi}}\subseteq\Delta$, whose morphisms are ordered forests composed by grafting. We define a full functor $\pi\colon \OrdFor\to\Delta_{\mathrm{epi}}^{op}$…
We define locally wide finitary 2-categories by relaxing the definition of finitary 2-categories to allow infinitely many objects and isomorphism classes of 1-morphisms and infinite dimensional hom-spaces of 2-morphisms. After defining…