This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases. A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.
Healthy ageing can lead to declines in both perceptual and cognitive functions. Impaired perception, such as that resulting from hearing loss or reduced visual or tactile resolution, increases demands on ‘higher-level’ cognitive functions to cope or compensate. It is possible, for example, to use focused attention to overcome perceptual limitations. Unfortunately, cognitive functions also decline in old age. This can mean that perceptual impairments are exacerbated by cognitive decline, and vice versa, but also means that interventions aimed at one type of decline can lead to improvements in the other. Just as improved cognition can ameliorate perceptual deficits, improving the stimulus can help offset cognitive deficits. For example, making directions and routes easy to follow can help compensate for declines in navigation abilities. In this Topic, we bring together papers from both auditory and visual researchers that address the interaction between perception and cognition in the ageing brain. Many of the studies demonstrate that a broadening of representations or increased reliance on gist underlie perceptual and cognitive age-related declines. There is also clear evidence that impaired perception is associated with poor cognition although, encouragingly, it can also be seen that good perception is associated with better cognition. Compensatory cognitive strategies were less successful in improving perception than might be expected. We also present papers which highlight important methodological considerations that are required when studying the older brain.
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Human language is the most powerful communication system that evolution has produced. Within this system, we can talk about things we can physically see, such as cats and tables, but also about more abstract entities, such as theories and feelings. But how are these abstract concepts grounded in human cognition and represented in the mind? How are they constructed in language? And how are they used in natural communication settings? This book addresses these questions through a collection of studies that relate to various theoretical frameworks, ranging from Conceptual Metaphor Theory to Words as Social Tools. Contributors investigate how abstract concepts are grounded in the mind, represented in language, and used in verbal discourse. This richness is matched by a range of methods used throughout the volume, from neuroimaging to computational modeling, and from behavioral experiments to corpus analyses.
First the concepts of [lambda]-presentable objects, locally [lambda]-presentable categories, and [lambda]-accessible categories are discussed in detail. The authors go on to prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapter they treat some advanced topics in model theory. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.
The series, founded in 1970, publishes works which either combine studies in the history of philosophy with a systematic approach or bring together systematic studies with reconstructions from the history of philosophy. Monographs are published in English as well as in German. The founding editors are Erhard Scheibe (editor until 1991), Günther Patzig (until 1999) and Wolfgang Wieland (until 2003). From 1990 to 2007, the series had been co-edited by Jürgen Mittelstraß.
With Applications to Wreath Products and Graphs. A Handbook for Students and Researchers
Author: Mati Kilp
Publisher: Walter de Gruyter
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany