The concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students. Firstly the properties of l-presentable objects, locally l-presentable categories, and l-accessible categories are discussed in detail, and the equivalence of accessible and sketchable categories is proved. The authors go on to study categories of algebras and prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapters they treat some topics in model theory and some set theoretical aspects. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.
We investigate properties of accessible categories with directed colimits and their relationship with categories arising from Shelah's Abstract Elementary Classes. We also investigate ranks of objects in accessible categories, and the effect of accessible functors on ranks.cardinals λ such that L is λ-categorical and, at the same time, a proper class of cardinals λ such that L is not λ-categorical.If this K has directed colimits then the categoricity conjecture fails for the class (4). By 4.12, however, this simple trick does not help for categories in class (3) of our hierarchy.Remark 6.4. Shelah's conjecture seems to be unknown even for finitely accessible categories, lying at level (1) of the hierarchy. It would be interesting to understand whether the exquisite Galois-theoretic machinery of [3] can be brought to bear implications in this setting.
The role of visual information and the precise nature of the representations used in the control of prehension movements has frequently been studied by having subjects reach for target objects in the absence of visual information. Such manipulations have often been described as preventing visual feedback; however, they also impose a working memory load not found in prehension movements with normal vision. In this study we examined the relationship between working memory and visuospatial attention using a prehension task. In this study six healthy, right-handed adult subjects reached for a wooden block under conditions of normal vision, or else with their eyes closed having first observed the placement of the target. Furthermore, the role of visuospatial attention was examined by studying the effect, on transport and grasp kinematics, of placing task-irrelevant "flanker" objects (a wooden cylinder) within the visual field on a proportion of trials. Our results clearly demonstrated that the position of flankers produced clear interference effects on both transport and grasp kinematics. Furthermore, interference effects were significantly greater when subjects reached to the remembered location of the target (i.e., with eyes closed). The finding that the position of flanker objects influences both transport and grasp components of the prehension movement is taken as support for the view that these components may not be independently computed and that subjects may prepare a coordinated movement in which both transport and grasp are specifically adapted to the task in hand. The finding that flanker effects occur primarily when reaching to the remembered location of the target object is interpreted as supporting the view that attentional processes do not work efficiently on working memory representations.
Abstract. We prove general results about completeness of cotorsion theories and existence of covers and envelopes in locally presentable abelian categories, extending the well-established theory for module categories and Grothendieck categories. These results are then applied to the categories of contramodules over topological rings, which provide examples and counterexamples.
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