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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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What tools, materials, and equipment do teachers work with?
Teachers work with a variety of tools, materials, and equipment in their daily work. Some common tools include whiteboards, markers, and projectors for delivering lessons. Materials such as textbooks, worksheets, and manipulatives are used to support student learning. Equipment like computers, printers, and audio-visual devices are also essential for creating engaging lessons and activities. Overall, teachers rely on a combination of traditional and modern tools to effectively educate their students.
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With which work tools, materials, and equipment do teachers work?
Teachers work with a variety of tools, materials, and equipment in their daily tasks. Some common tools include computers, projectors, whiteboards, and pens. Materials can range from textbooks and worksheets to art supplies and science equipment. Additionally, teachers may use equipment such as printers, laminators, and document cameras to enhance their teaching methods and create engaging learning experiences for students.
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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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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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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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Incirliev - Special Category
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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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Which porn category is meant?
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What would be a suitable title for tools, equipment, materials, and workplace safety?
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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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