Related papers: Higher-dimensional study of extensions via torsors

Cohomology of a topological space with coefficients in stacks of abelian 2-groups is considered. A 2-categorical analog of the theorem of Grothendieck is proved, relating cohomology of the space with coefficients in a 2-stage spectrum and…

For a variety X which admits a Cox ring we introduce a functor from the category of quasi-coherent sheaves on $X$ to the category of graded modules over the homogeneous coordinate ring of $X$. We show that this functor is right-adjoint to…

The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…

In this paper we consider the problem of classifying the isomorphism classes of extensions of degree pk of a p-adic field, restricting to the case of extensions without intermediate fields. We establish a correspondence between the…

We consider $H$(eisenberg)-type groups whose law of left translation gives rise to a bracket generating distribution of step 2. In the contrast with sub-Riemannian studies we furnish the horizontal distribution with a nondegenerate…

We define a dimension for a triangulated category. We prove a representabilityTheorem for a certain class of functors on finite dimensional triangulatedcategories. We study the dimension of the boundedderived category of an algebra or a…

Let $S$ be a scheme such that $2$ is not a zero divisor. In this paper, we address the following question: given a quadratic algebra over $S$, how can we parametrize its Picard group in terms of quadratic forms? In 2011, Wood established a…

Classical homological algebra considers chain complexes, resolutions, and derived functors in additive categories. We describe "track algebras in dimension n", which generalize additive categories, and we define higher order chain…

We develop a general theory of (extended) inner autoequivalences of objects of any 2-category, generalizing the theory of isotropy groups to the 2-categorical setting. We show how dense subcategories let one compute isotropy in the presence…

We prove that the homotopy theory of Picard 2-categories is equivalent to that of stable 2-types.

We study the homotopy category $\mathsf{K}_{N}(\mathcal{B})$ of $N$-complexes of an additive category $\mathcal{B}$ and the derived category $\mathsf{D}_{N}(\mathcal{A})$ of an abelian category $\mathcal{A}$. First we show that both…

Torsors under affine groups are generalized in the super context by super-torsors under affine super-groups. We investigate those super-torsors by using Hopf-algebra language and techniques. It is explicitly shown, under suitable…

In this paper, we go into the study of the 2-category SSS_\Sigma of \Sigma-constructible stacks. The notions of constructible stack was introduced by D. Treumann. It is a natural generalization of constructible sheaf. D. Treumann has also…

We extend the usual notion of parallel transport along a path to triangulated surfaces. A homotopy of paths is lifted into a fibered category with connection and this defines a functor between the fibers above the boundary paths. These…

Exploiting the symmetry topological field theory/topological order correspondence (SymTFT/TO), together with the higher-categorical structure of 6D N =(2,0) SCFTs, we prove that the total quantum dimension of the relative gaugeable algebra…

The purpose of this paper is to give some solutions for the classification problem in fibration theory by using the homotopy sequences of fibrations (sequences of $n$-th homotopy groups $ \pi_{n}(S,s_{o}) $ of total spaces of fibrations).…

This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between…

We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of what we call `spider moves'. We then create a category…

We outline a proof that the stack of symplectic toric G-manifolds over a fixed orbit space W is a torsor for the stack of symplectic toric G-principal bundles over W.

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We…