Related papers: Obstructions for gluing biset functors
Given a central extension of Lie groups, we study the classification problem of lifting the structure group together with a given connection. For reductive structure groups we introduce a new connective structure on the lifting gerbe…
Given a (smooth) action of a Lie group G on Rd we construct a DGA whose Maurer-Cartan elements are in one to one correspondence with some class of defomations of the (induced) G-action on the ring of formal power series with coefficients in…
We generalise the construction of the Lie algebroid of a Lie groupoid so that it can be carried out in any tangent category. First we reconstruct the bijection between left invariant vector fields and source constant tangent vectors based…
A covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor…
For any finite group G, we define a bivariant functor from the Dress category of finite G-sets to the conjugation biset category, whose objects are subgroups of G, and whose morphisms are generated by certain bifree bisets. Any additive…
A class of topological spaces is topologically rigid if any two spaces with the same fundamental group are also homeomorphic. Topological rigidity, in addition to its intrinsic interest, has been useful for solving abstract commensurability…
We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are…
We present a novel approach to the concept of gluing in mathematics by introducing the notions of a gluing data category and a gluing data functor. Our work provides a formal categorical characterization of the notion of gluing in algebraic…
Suppose that $G$ is a locally compact group and $\pi$ is a (not necessarily irreducible) unitary representation of a closed normal subgroup $N$ of $G$ on a Hilbert space $H$. We extend results of Clifford and Mackey to determine when $\pi$…
Compositionality is at the heart of computer science and several other areas of applied category theory such as computational linguistics, categorical quantum mechanics, interpretable AI, dynamical systems, compositional game theory, and…
Strong approximation with Brauer-Manin obstruction is established for smooth varieties containing a connected linear algebraic group with a compatible action.
The paper provides computations of the first non-vanishing $\mathbb{A}^1$-homotopy sheaves of the orthogonal Stiefel varieties which are relevant for the unstable isometry classification of quadratic forms over smooth affine schemes over…
We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors ?^{**} and D tensor ^{**}? tensor D^{-1}. This…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
We provide an extension of the Gromov--Zimmer Embedding Theorem for Cartan geometries of [3] to tractor bundles carrying any invariant connection, including tractor connections and prolongation connections of first BGG operators for…
In this article, we develop a general technique for gluing subcategories of $\infty$-categories. We obtain categorical equivalences between simplicial sets associated to certain multisimplicial sets. Such equivalences can be used to…
We consider the general problem of deforming a surjective map of modules $f : E \to F$ over a coproduct sheaf of rings $B=B_1 \otimes_A B_2$ when the domain module $E = B_1 \otimes_A E_2$ is obtained via extension of scalars from a…
This paper continues the development of the deformation theory of abelian categories introduced in a previous paper by the authors. We show first that the deformation theory of abelian categories is controlled by an obstruction theory in…
We propose an alternative definition for families of stable pairs $(X,D)$ over a possibly non-reduced base when $D$ is reduced, by replacing $(X,D)$ with an appropriate orbifold pair $(\mathcal X,\mathcal D)$. This definition of a stable…
We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in…