We prove that Keimel and Lawson's K-completion Kc of the simple valuation monad Vs defines a Kc∘Vs on each -category K. also characterise Eilenberg-Moore algebras as weakly locally convex K-cones, its algebra morphisms continuous linear maps. In addition, we explicitly describe distributive law over Kc, which allows us to show any (resp., convex, linear) topological cone is K-cone. give an exam...

Top-k queries are useful in retrieving top-k records from a given set of records depending on the value of a function F on their attributes. Many techniques have been proposed in database literature for answering top-k queries. These are mainly categorized into three: Sorted-list based, layer based and View based. In first category, records are sorted along each dimension and then assigned a ra...

Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 then it is the compact derived category of the dual numbers over k. As main results of the paper we show that for w ≤ 0, the category T has no non-trivial t-structures, but ...

In this announcement we describe categories of equivariant vector bundles on certain “spherical” varieties. Our description is in linear-algebra terms: vector spaces equipped with filtrations, group and Lie-algebra actions, and linear maps preserving these structures. The two parents of our description are i) the description of G-equivariant vector bundles on homogeneous spaces G/H as H-represe...

The regular representation of an essentially finite 2-group G in the 2-category 2Vectk of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology invariants classifying it computed. It is next shown that all hom-categories in Rep 2Vectk pGq are 2-vector spaces under quite standard assumptions on the field k, and a formula giving the corresponding “intertwining numbers” is obtained wh...

By an F -semi-linear G-representation we mean an F -space V with a (k-linear) G-action such that (a v) = a v for any 2 G, v 2 V and a 2 F . This is the same as a module over the algebra F hGi := F ZZ[G] with evident action of F and the diagonal action of G. If G acts on F faithfully, then F hGi is a central k-algebra. Semi-linear G-representations nite-dimensional over F form an abelian tensor ...

We show that the category FinVectk of finite dimensional vector spaces and linear maps over any field k is (collectively) complete for the traced symmetric monoidal category freely generated from a signature, provided that the field has characteristic 0; this means that for any two different arrows in the free traced category there always exists a strong traced functor into FinVectk which disti...

let $a$ be a nite dimensional $k-$algebra and $r$ be a locally bounded category such that $r rightarrow r/g = a$ is a galois covering dened by the action of a torsion-free group of automorphisms of $r$. following [30], we provide criteria on the convex subcategories of a strongly simply connected category r in order to be a cycle- nite category and describe the module category of $a$. we pro...