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Category Theory
Category theory is a branch of abstract algebra with incredibly diverse applications.This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied.Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership.Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised.The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads.An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories.Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.
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Research on Functional Grammar of Chinese II : Reference and Grammatical Category
The functional perspective on Chinese syntax has yielded various new achievements since its introduction to Chinese linguistics in the 1980s. This two-volume book is one of the earliest and most influential works to study the Chinese language using functional grammar.With local Beijing vernacular (Pekingese) as a basis, the information structure and focus structure of the Chinese language are systematically examined.By using written works and recordings from Beijingers, the authors discuss topics such as the relationship between word order and focus, and the distinction between normal focus and contrastive focus. In addition, the authors also subject the reference and grammatical categories of the Chinese language to a functional scrutiny while discussion of word classes and their functions creatively combines modern linguistic theories and traditional Chinese linguistic theories.This book will be of interest to students and scholars of Chinese linguistics and linguistics in general.
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Starting Category Theory
One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples.This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs.It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples.Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.Starting Category Theory serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study.Most crucially, it deliberately caters to those who are new to category theory, not requiring readers to have a background in pure mathematics, but only a basic understanding of linear algebra.
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Handbook of Research on Science Teacher Education
This groundbreaking handbook offers a contemporary and thorough review of research relating directly to the preparation, induction, and career long professional learning of K–12 science teachers. Through critical and concise chapters, this volume provides essential insights into science teacher education that range from their learning as individuals to the programs that cultivate their knowledge and practices.Each chapter is a current review of research that depicts the area, and then points to empirically based conclusions or suggestions for science teacher educators or educational researchers.Issues associated with equity are embedded within each chapter.Drawing on the work of over one hundred contributors from across the globe, this handbook has 35 chapters that cover established, emergent, diverse, and pioneering areas of research, including: Research methods and methodologies in science teacher education, including discussions of the purpose of science teacher education research and equitable perspectives; Formal and informal teacher education programs that span from early childhood educators to the complexity of preparation, to the role of informal settings such as museums; Continuous professional learning of science teachers that supports building cultural responsiveness and teacher leadership; Core topics in science teacher education that focus on teacher knowledge, educative curricula, and working with all students; and Emerging areas in science teacher education such as STEM education, global education, and identity development. This comprehensive, in-depth text will be central to the work of science teacher educators, researchers in the field of science education, and all those who work closely with science teachers.
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The Category Management Handbook
Category management is one of the biggest contributors of commercial value in the area of procurement and supply chain.With a proven track record of successful delivery since the early 1990s, it helps organisations gather and analyse key data about their procurement spend before subsequently creating and delivering value-adding strategies that change the value proposition from supply chains.The aim of category management is to find long-term breakthrough strategies that help lift an organisation’s commercial performance to a new level. Because of its strategic long-term orientation and complex execution, category management has long been the preserve of commercial consulting companies – in effect a ‘black box’ toolkit shrouded in expensive methodologies. This practical handbook lifts the lid on category management by providing readers with a step-by-step process and established toolkit that allows them a ‘do-it-yourself’ approach.Each activity is presented as a simple tool or technique for practitioners to apply to their own organisations.To support each activity, easy-to- use templates and checklists have been provided, together with simple but practical hints and tips for implementation. This handbook is a ‘must read’ for all procurement and supplychain managers looking to find significant improvements in their organisations.Its practical approach cuts through long-winded consultant-speak and provides an easy-to-use practical toolkit for everyday application.
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