Related papers: Fundamental groupoids for simplicial objects in Ma…

Let $A$ be a unital associative algebra over a field $k$. All unital associative algebras containing $A$ as a subalgebra of a given codimension $\mathfrak{c}$ are described and classified. For a fixed vector space $V$ of dimension…

We study Quillen's model category structure for homotopy of simplicial objects in the context of Janelidze, Marki and Tholen's semi-abelian categories. This model structure exists as soon as the base category A is regular Mal'tsev and has…

For connected reductive groups together with a Frobenius root $F$, we show that the cohomology of the structure sheaf and respectively the canonical sheaf for compactified Deligne--Lusztig varieties associated to an element in the free…

Let $F$ be a field of characteristic $0$ containing all roots of unity. We construct a functorial compact Hausdorff space $X_F$ whose profinite fundamental group agrees with the absolute Galois group of $F$, i.e. the category of finite…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We introduce the first provably efficient algorithm to check if a finitely generated subgroup of an almost simple semi-simple group over the rationals is Zariski-dense. We reduce this question to one of computing Galois groups, and to this…

In this paper we study the classifying spaces of graph products of simplicial groups and connected Hopf algebras over a field, and show that they can be uniformly treated under the framework of polyhedral products. It turns out that these…

We prove that the specialization to q=1 of a Kirillov-Reshetikhin module for an untwisted quantum affine algebra of classical type is projective in a suitable category. This yields a uniform character formula for the Kirillov-Reshetikhin…

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

We solve the integration problem for generalized complex manifolds, obtaining as the natural integrating object a weakly holomorphic symplectic groupoid, which is a real symplectic groupoid with a compatible complex structure defined only…

We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using…

Let $M$ be a factor with separable predual and $G$ a compact group of automorphisms of $M$ whose action is minimal, i.e. $M^{G^\prime}\cap M = C$, where $M^G$ denotes the $G$-fixed point subalgebra. Then every intemediate von Neumann…

We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions,…

We define a linear structure on Grothendieck's arithmetic fundamental group $\pi_1(X, x)$ of a scheme $X$ defined over a field $k$ of characteristic 0. It allows us to link the existence of sections of the Galois group ${\rm Gal}(\bar k/k)$…

Consider a reductive group G over a non-archimedean local field. The Galois group Gal(C/Q) acts naturally on the category of smooth complex G-representations. We prove that this action stabilizes the class of standard modules. This…

{\em Galois comodules} over a coring can be characterised by properties of the relative injective comodules. They motivated the definition of {\em Galois functors} over some comonad (or monad) on any category and in the first section of the…

We extend the model structure on the category $\mathbf{Cat}(\mathcal{E})$ of internal categories studied by Everaert, Kieboom and Van der Linden to an algebraic model structure. Moreover, we show that it restricts to the category of…

Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad…

In previous work, we showed that there are appropriate model category structures on the category of simplicial categories and on the category of Segal precategories, and that they are Quillen equivalent to one another and to Rezk's complete…

A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial 1-complexes, or graphs, very much in the spirit of Stallings. A number of classical, as well as some new results about…