相关论文: Virtual concepts in the theory of accessible categ…

Using full images of accessible functors, we prove some results about combinatorial and accessible model categories. In particular, we give an example of a weak factorization system on a locally presentable category which is not accessible.

Fix a set-theoretic universe $V$. We look at small extensions of $V$ as generalised degrees of computability over $V$. We also formalise and investigate the complexity of certain methods one can use to define, in $V$, subclasses of degrees…

We give a new characterisation of virtually free groups using graph minors. Namely, we prove that a finitely generated, infinite group is virtually free if and only if for any finite generating set, the corresponding Cayley graph is minor…

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

The ubiquitous nature of modern Information Retrieval and Virtual World give rise to new realities. To what extent are these "realities" real? Which "physics" should be applied to quantitatively describe them? In this essay I dwell on few…

An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the…

We revisit an old assertion due to Rouquier, characterizing the perfect complexes as bounded homological functors on the bounded complexes of coherent sheaves. The new results vastly generalize the old statement---first of all the ground…

In this article we revisit the concept of abstraction as it is used in visualization and put it on a solid formal footing. While the term \emph{abstraction} is utilized in many scientific disciplines, arts, as well as everyday life,…

We define a generalization of virtual links to arbitrary dimensions by extending the geometric definition due to Carter et al. We show that many homotopy type invariants for classical links extend to invariants of virtual links. We also…

This is the final version of a series of papers uploaded in May 25, 2005. We have splitted the long last paper of the previous version in two parts to make it easier to understand. The results are essentially the same, although the…

The rules governing the essentially algebraic notion of a category with families have been observed (independently) by Steve Awodey and Marcelo Fiore to precisely match those of a representable natural transformation between presheaves.…

If $G$ is a group, a virtual retract of $G$ is a subgroup which is a retract of a finite index subgroup. Most of the paper focuses on two group properties: property (LR), that all finitely generated subgroups are virtual retracts, and…

We show that an abelian category can be exactly, fully faithfully embedded into a module category as the right perpendicular subcategory to a set of modules or module morphisms if and only if it is a locally presentable abelian category…

The point of this paper is to prove the conjecture that virtual 2-vector bundles are classified by K(ku), the algebraic K-theory of topological K-theory. Hence, by the work of Ausoni and the fourth author, virtual 2-vector bundles give us a…

We investigate a possible category theoretical description for agent based modeling by outlining justifications for two main principles to describe the valuations in a realistic way in microeconomics: 1) It is assumed that the valuations…

Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…

This is a continuation of the paper "Modular tensor categories and orbifold theories", arXiv:math.QA/0104242. It discusses orbifold models of conformal filed theory, or, in mathematical language, question of constructing the category of…

We study properties of relative modular categories and derive sufficient conditions for their existence. In particular, we derive sufficient conditions for relative pre-modular categories to be non-degenerate and relative modular, and for…

In this paper we continue with the algebraic study of Krivine's realizability, refining some of the authors' previous constructions by introducing two categories, with objects the abstract Krivine structures and the implicative algebras…