Elements of ∞-Category Theory PDF Download
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Author: Emily Riehl
Publisher: Cambridge University Press
ISBN: 1108952194
Category : Mathematics
Languages : en
Pages : 782
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Book Description
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.
Author: Anthony Kennada
Publisher: John Wiley & Sons
ISBN: 111961161X
Category : Business & Economics
Languages : en
Pages : 170
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Book Description
Lessons from HubSpot, Salesforce, Gainsight and Other Iconic Brands "The Uber of this" "The Salesforce of that" "It's like Instagram, but for..." There is no such thing as an original idea anymore – right? Actually, it turns out that the world’s most innovative companies have created so much more than just brand new products and technology. They've created entirely new market categories. The challenge is that successfully building new categories requires a perfect storm of luck and timing. Or does it? Category Creation is the first and only book on the topic written by executives and marketers actively building new categories. It explains how category creation has become the Holy Grail of marketing, and more importantly, how it can be planned and orchestrated. It's not about luck. You can use the same tactics that other category-defining companies have used to delight customers, employees, and investors. There’s no better strategy that results in faster growth and higher valuations for the company on top. Author Anthony Kennada, former Chief Marketing Officer at Gainsight, explains how he led Gainsight in creating the “customer success” category, and shares success stories from fellow category-creators like Salesforce, HubSpot and others. It requires much more than just having the best product. You have to start and grow a conversation that doesn’t yet exist, positioning a newly discovered problem in addition to your company and product offerings. The book explains the 7 key principles of category creation, including the importance of creating a community of early adopters who will rally around the problem they all share—especially if someone will lead them. · Identify the “go” and “no go” signals for category creation in your business · Activate customers and influencers as brand ambassadors · Grow a community by investing in live events and experiences · Prove the impact of category creation investments on growth, customer success, and company culture Written for entrepreneurs, marketers, and executives from startups to large enterprises, Category Creation is the exclusive playbook for building a category defining brand in the modern economy.
Author: Ricky Tucker
Publisher: Beacon Press
ISBN: 0807003492
Category : Social Science
Languages : en
Pages : 256
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Book Description
An Electric Literature “Most Anticipated LGBTQ+ Book of 2022” Selection A love letter to the legendary Black and Latinx LGBTQ underground subculture, uncovering its abundant legacy and influence in popular culture. What is Ballroom? Not a song, a documentary, a catchphrase, a TV show, or an individual pop star. It is an underground subculture founded over a century ago by LGBTQ African American and Latino men and women of Harlem. Arts-based and intersectional, it transcends identity, acting as a fearless response to the systemic marginalization of minority populations. Ricky Tucker pulls from his years as a close friend of the community to reveal the complex cultural makeup and ongoing relevance of house and Ballroom, a space where trans lives are respected and applauded, and queer youth are able to find family and acceptance. With each chapter framed as a “category” (Vogue, Realness, Body, et al.), And the Category Is . . . offers an impressionistic point of entry into this subculture, its deeply integrated history, and how it’s been appropriated for mainstream audiences. Each category features an exclusive interview with fierce LGBTQ/POC Ballroom members—Lee Soulja, Benjamin Ninja, Twiggy Pucci Garçon, and more—whose lives, work, and activism drive home that very category. At the height of public intrigue and awareness about Ballroom, thanks to TV shows like FX’s Pose, Tucker’s compelling narratives help us understand its relevance in pop culture, dance, public policy with regard to queer communities, and so much more. Welcome to the norm-defying realness of Ballroom.
Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 272
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Book Description
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.
Author: Robert J. Glushko
Publisher: "O'Reilly Media, Inc."
ISBN: 1491911719
Category : Computers
Languages : en
Pages : 560
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Book Description
Note about this ebook: This ebook exploits many advanced capabilities with images, hypertext, and interactivity and is optimized for EPUB3-compliant book readers, especially Apple's iBooks and browser plugins. These features may not work on all ebook readers. We organize things. We organize information, information about things, and information about information. Organizing is a fundamental issue in many professional fields, but these fields have only limited agreement in how they approach problems of organizing and in what they seek as their solutions. The Discipline of Organizing synthesizes insights from library science, information science, computer science, cognitive science, systems analysis, business, and other disciplines to create an Organizing System for understanding organizing. This framework is robust and forward-looking, enabling effective sharing of insights and design patterns between disciplines that weren’t possible before. The Professional Edition includes new and revised content about the active resources of the "Internet of Things," and how the field of Information Architecture can be viewed as a subset of the discipline of organizing. You’ll find: 600 tagged endnotes that connect to one or more of the contributing disciplines Nearly 60 new pictures and illustrations Links to cross-references and external citations Interactive study guides to test on key points The Professional Edition is ideal for practitioners and as a primary or supplemental text for graduate courses on information organization, content and knowledge management, and digital collections. FOR INSTRUCTORS: Supplemental materials (lecture notes, assignments, exams, etc.) are available at http://disciplineoforganizing.org. FOR STUDENTS: Make sure this is the edition you want to buy. There's a newer one and maybe your instructor has adopted that one instead.
Author: Lainey Cameron
Publisher: The Wild Rose Press Inc
ISBN: 1509231390
Category : Fiction
Languages : en
Pages : 338
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Book Description
Silicon Valley investor Ryn Brennan is on the verge of achieving everything she dreamed. She's succeeded in the male-dominated venture capital world, has a supportive husband, and is about to close the deal of her career. Everything is going exactly as planned, until she meets Carly, her husband's mistress, across the negotiating table. Carly clawed her way back from being a teenage runaway to become an accomplished scientist, caring single mom, and co-founder of her startup. Once she marries her loving fiancé, she'll secure the complete family she craves. But she's blindsided to discover her not so perfect fiancé is already married—to Ryn, her company's biggest investor. In an industry full of not-so-subtle sexism, can the two women rise above, and work together to overcome heartbreak, and ensure their success?
Author: Emily Riehl
Publisher: Cambridge University Press
ISBN: 1108952194
Category : Mathematics
Languages : en
Pages : 782
Get Book
Book Description
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.
Author: Brendan Fong
Publisher: Cambridge University Press
ISBN: 1108482295
Category : Computers
Languages : en
Pages : 351
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Book Description
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
Author: Amnon Neeman
Publisher: Princeton University Press
ISBN: 9780691086866
Category : Mathematics
Languages : en
Pages : 468
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Book Description
The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among other material, some remarkable improvements on Brown's classical representability theorem. In addition, the author introduces a class of triangulated categories"--the "well generated triangulated categories"--and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated, and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra, algebraic geometry, homotopy theory, and mathematical physics.
Author: Birgit Richter
Publisher: Cambridge University Press
ISBN: 1108847625
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
Author: Pavel Etingof
Publisher: American Mathematical Soc.
ISBN: 1470434415
Category : Algebraic topology
Languages : en
Pages : 344
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Book Description
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
