Related papers: Leibnizian, Robinsonian, and Boolean Valued Monads
In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the literature. We also study the relation between various…
A relative Picard theory in the context of graded manifolds is introduced. A Berezinian calculus and a theory of connections over SUSY-curves are systematically developed, and used to prove a Gauss-Bonnet theorem for line bundles in that…
For a generalisation of the classical theory of Hopf algebra over fields, A. Brugui\`eres and A. Virelizier study opmonoidal monads on monoidal categories (which they called {\em bimonads}). In a recent joint paper with S. Lack the same…
We study the concept of idempotence for relative monads, which exhibits several subtleties not present for non-relative monads. In particular, there is a bifurcation of notions of idempotence in the relative setting, which are…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
We construct Boolean Algebras answering questions of Monk on cardinal invariants. The results are proved in ZFC (rather than giving consistency results). We deal with the existence of superatomic Boolean Algebras with ``few automorphisms'',…
We introduce an equivalence relation, called cobordism, for words and study cobordism invariants of words inspired by methods of low-dimensional topology.
We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number…
There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level…
In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…
In this paper we give the classification of rank 3 vector bundles without "inner" cohomology on a quadric hypersurface \Q_n (n>3) by studying the associated monads.
We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate some new cardinal invariants.
Ladders of recollements of abelian categories are introduced, and used to address three general problems. Ladders of a certain height allow to construct recollements of triangulated categories, involving derived categories and singularity…
In this paper we continue the investigation of Loday's Leibniz cohomology as a new invariant for differentiable manifolds. In particular the Leibniz coboundary of a k-tensor (in the sense of differential geometry) is computed in a local…
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their…
Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us…
Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…
Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…
A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…