Take for instance a k-algebra 4 over a field k. Then the usual k-dual DM=Homk(M, k) of a finite dimensional 4-module M satisfies all three properties. However for infinite dimensional 4-modules the condition (D1) does not hold, and for most rings there is even on the level of the finite length modules no duality functor between right and left modules available. The aim of this note is to descri...

It is shown that the “constant sheaves” functor ∇ : Sets → Eff does not preserve 1-filtered colimits, and that as a consequence of this, the full subcategory of Eff on the countable projective objects is not dense. © 2005 Elsevier B.V. All rights reserved.

In this paper a notion of generalized 2-vector space is introduced which includes Kapranov and Voevodsky 2-vector spaces. Various kinds of generalized 2-vector spaces are considered and examples are given. The existence of non free generalized 2-vector spaces and of generalized 2-vector spaces which are non Karoubian (hence, non abelian) categories is discussed, and it is shown how any generali...

Abstract. Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal. Hovey gave a bijection between the set of coherent subcategories of the category of finitely presented R-modules and the set of thick subcategories of the derived category of perfect R-complexes. Using this isomorphism, he proved that every coherent subcategory of finitely presented R-module...

We construct a functor from the derived category of homotopy Gerstenhaber algebras, g, with finite-dimensional cohomology to the purely geometric category of so-called F ∞-manifolds. The latter contains Frobenius manifolds as a subcategory (so that a pointed Frobenius manifold is itself a homotopy Gerstenhaber algebra). If g happens to be formal as a L ∞-algebra, then its F ∞-manifold comes equ...

We consider orbifolds as diffeological spaces. This gives rise to a natural notion of differentiable maps between orbifolds, making them into a subcategory of diffeology. We prove that the diffeological approach to orbifolds is equivalent to Satake’s notion of a V-manifold and to Haefliger’s notion of an orbifold. This follows from a lemma: a diffeomorphism (in the diffeological sense) of finit...

Let C be a full subcategory of the category of topological abelian groups and SPC denote the full subcategory of subobjects of products of objects of C. We say that SPC has Mackey coreeections if there is a functor that assigns to each object A of SPC an object A that has the same group of characters as A and is the nest topology with that property. We show that the existence of Mackey coreeect...

The notions of central ring actions and support in triangulated categories have proved quite fruitful recently, cf. [1], [2], [3], [4]. They unify ideas and techniques from group cohomology, commutative ring theory (complete intersections) and Hochschild cohomology. This brief survey is an introduction to the basic concepts. Let T be a triangulated category with suspension functor Σ. A subcateg...

This paper undertakes a review and classification of the mobile business (m-business) theme of mobile computing research, with the intention of identifying the dominant issues and conceptual approaches to existing research. It consists of 100 articles published between 2005 and 2012 in a diverse journals focused on information systems, business, and development. The papers are reviewed under th...