A 2023 Lambda Literary Award Finalist in Nonfiction 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.

An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.

A short introduction ideal for students learning category theory for the first time.

A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.

These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications. Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras. Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.

Comprises six presentations on new developments in category theory from the March 1997 workshop. The topics are categorification, computads for finitary monads on globular sets, braided n- categories and a-structures, categories of vector bundles and Yang- Mills equations, the role of Michael Batanin's monoidal globular categories, and braided deformations of monoidal categories and Vassiliev invariants. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

This monograph introduces involutive categories and involutive operads, featuring applications to the GNS construction and algebraic quantum field theory. The author adopts an accessible approach for readers seeking an overview of involutive category theory, from the basics to cutting-edge applications. Additionally, the author’s own recent advances in the area are featured, never having appeared previously in the literature. The opening chapters offer an introduction to basic category theory, ideal for readers new to the area. Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author’s state-of-the-art research. Chapters on coherence of involutive symmetric monoidal categories, and categorical GNS construction follow. The last chapter covers involutive operads and lays important coherence foundations for applications to algebraic quantum field theory. With detailed explanations and exercises throughout, Involutive Category Theory is suitable for graduate seminars and independent study. Mathematicians and mathematical physicists who use involutive objects will also find this a valuable reference.

Retail shelf management means cost-efficiently aligning retail operations with consumer demand. As consumers expect high product availability and low prices, and retailers are constantly increasing product variety and striving towards high service levels, the complexity of managing retail business and its operations is growing enormously. Retailers need to match consumer demand with shelf supply by balancing variety (number of products) and service levels (number of items of a product), and by optimizing demand and profit through carefully calibrated prices. As a result the core strategic decisions a retailer must make involve assortment sizes, shelf space assignment and pricing levels. Rigorous quantitative methods have emerged as the most promising solution to this problem. The individual chapters in this book therefore focus on three areas: (1) combining assortment and shelf space planning, (2) providing efficient decision support systems for practically relevant problem sizes, and (3) integrating inventory and price optimization into shelf management.

Approach purchasing and procurement strategically, effectively and sustainably, with this comprehensive and practical guide to category management. Category Management in Purchasing equips those working in procurement with the tools they need to ensure effective procurement in an ever changing landscape. Combining practical advice and theory, this essential resource is crucial for developing successful purchasing strategies. Covering new technology-driven approaches to category management, this new edition outlines digital transformations and technological advancements, from digital sourcing platforms to new tools and systems. This edition also provides readers with the knowledge to approach complex sourcing situations not only effectively, but also sustainably. Including new guidance on how organizations and businesses can implement sustainability into their procurement strategies, Jonathan O'Brien recontextualizes category management in a time when responsible sourcing is more important than ever. This highly regarded and essential text provides what everyone in procurement needs when striving to make category management a reality.