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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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Temporary Migration : Category of Analysis or Category of Practice?
Temporariness has become an increasingly salient feature in international migration that presents itself as fragmented, non-linear, including different intermediate stops and multiple returns and new departures.This book proposes a new analytical framework that brings together the role of policies defining migrants as temporary and the role of migrant’s own agency in perceiving their migration project as temporary or permanent.The proposed analytical framework is conceived taking into account both low-skill and high-skilled, legal and irregular migratory flows, and also different visa and citizenship regimes.The aim of this book is to highlight the interplay between the lived reality and the policy and legal concepts on temporary migration and point out to the tensions and contradictions inherent in the latter.Contributions to this book cover different country cases including Canada, Australia, Nepal, Taiwan and Germany, Italy, Russia, and several former Soviet Republics as well as a variety of sectors ranging from opera singers to construction and domestic workers. This book will be a key resource for academics, researchers, and advanced students of sociology, politics, law, migration studies, and ethnic and racial studies.It was originally published as a special issue of the Journal of Ethnic and Migration Studies.
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Basic Category Theory
At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics.After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal properties: via adjoint functors, representable functors, and limits.A final chapter ties all three together. The book is suitable for use in courses or for independent study.Assuming relatively little mathematical background, it is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time.For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics.At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations.Copious exercises are included.
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Which secure website can I use for a cheats app in the gaming category?
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What is a product category?
A product category is a group of products that are related to each other based on their function, usage, or target market. It is a way to classify and organize similar products for consumers and businesses. For example, the electronics product category includes items such as smartphones, laptops, and tablets. Product categories help consumers and businesses navigate through a wide range of products and make informed purchasing decisions.
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What is the sex category?
The sex category refers to the classification of individuals as male or female based on their biological characteristics, such as reproductive organs and chromosomes. This classification is typically assigned at birth and is used to differentiate between male and female individuals in various contexts, including healthcare, sports, and legal documentation. It is important to note that sex is distinct from gender, which refers to the social and cultural roles, behaviors, and identities associated with being male or female.
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What is your favorite category?
As an AI, I don't have personal preferences, but I can help you with a wide range of categories such as science, history, technology, and more. Let me know what you're interested in, and I'll be happy to assist you!
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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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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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Abelian Model Category Theory
Offering a unique resource for advanced graduate students and researchers, this book treats the fundamentals of Quillen model structures on abelian and exact categories.Building the subject from the ground up using cotorsion pairs, it develops the special properties enjoyed by the homotopy category of such abelian model structures.A central result is that the homotopy category of any abelian model structure is triangulated and characterized by a suitable universal property – it is the triangulated localization with respect to the class of trivial objects.The book also treats derived functors and monoidal model categories from this perspective, showing how to construct tensor triangulated categories from cotorsion pairs.For researchers and graduate students in algebra, topology, representation theory, and category theory, this book offers clear explanations of difficult model category methods that are increasingly being used in contemporary research.
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An Introduction to Category Theory
Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics.Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject.Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory.It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions.The material is slowly developed using many examples and illustrations to illuminate the concepts explained.Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study.It can also be used as a recommended text for a taught introductory course.
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Which porn category is meant?
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Under what category does Saw fall?
Saw falls under the category of horror and thriller films. The franchise is known for its graphic violence, intense suspense, and psychological elements, which are characteristic of the horror genre. The films also often involve a serial killer who sets up elaborate traps and games for his victims, adding a thriller aspect to the storyline. Overall, Saw is a prominent example of the horror-thriller genre in the film industry.
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What is your favorite Olympic category?
As an AI, I don't have personal preferences, but I can tell you that many people enjoy watching the gymnastics category in the Olympics. The combination of strength, agility, and grace displayed by the athletes is truly impressive. The gymnastics events, such as the floor exercise, balance beam, and uneven bars, showcase the incredible athleticism and skill of the competitors. It's always thrilling to see the athletes push the boundaries of what the human body can achieve.
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To which category do subliminals belong?
Subliminals belong to the category of psychological techniques or stimuli that are designed to influence the subconscious mind without the individual being consciously aware of it. They are often used in advertising, self-improvement programs, and therapy to promote certain behaviors, thoughts, or beliefs. Subliminals work by bypassing the conscious mind and targeting the subconscious, where they can potentially have a subtle but powerful impact on an individual's thoughts and behaviors.
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