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Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. The authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience, the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. For all algebraists and category theorists this book will be a rewarding read.

Galois Theories | Borceux Francis | Paperback | Twarda

Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small categories enriched over the extended real half-line. Hence, equipped with a quantale V replacing the reals and a monad T replacing the ultrafilter monad laxly extended from set maps to V-valued relations, the book develops a categorical theory of T, V-algebras that is inspired simultaneously by its metric and topological roots. The book highlights in particular the distinguished role of equationally defined structures within the given lax-algebraic context and presents numerous new results ranging from topology and approach theory to domain theory. All the necessary pre-requisites in order and category theory are presented in the book

Monoidal Topology | Hofmann Dirk | Twarda | Twarda

The book is extremely pleasant to read, with masterfully crafted exercises and examples that create a beautiful and unique thread of presentation leading the reader safely into the wonderfully rich, expressive, and powerful theory of categories. -- The Math Association br Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, and other topics. br Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad ran

Category Theory in Context | Riehl Emily | Paperback | Twarda

pemKey Categories in the Study of Religion emexplores the symbiotic relationship between context and critique. This volume centers on four key contextual categories that stand at the heart of the academic study of religion citizenship and politics, class and economy, gender and sexuality, and race and ethnicity. The contributors to this volume investigate the ways that method, theory, and data are mobilized via context as a primary impetus for critical analysis.ppbrppUsing these key categories, this volume brings together diverse data domains to explore the similarities and differences that emerge when one theoretical framework moves from domain to domain. In the same way that scholars have argued against an essentialist understanding of religion, these categories of analysis should be employed within the matrix of their social, cultural, and ideological contexts.ppbrppEach of the four parts begins with an orienting essay that investigates a category, analyzing the construction of cate

Key Categories in the Study of Religion | King Rebekka | Twarda

iHistoricizing Feari is a historical interrogation of the use of fear as a tool to vilify and persecute groups and individuals from a global perspective, offering an unflinching look at racism, fearful framing, oppression, and marginalization across human history.The book examines fear and Othering from a historical context, providing a better understanding of how power and oppression is used in the present day. p Contributors ground their work in the theory of Othering--the reductive action of labeling a person as someone who belongs to a subordinate social category defined as the Other--in relation to historical events, demonstrating that fear of the Other is universal, timeless, and interconnected. Chapters address the music of neo-Nazi white power groups, fear perpetuated through the social construct of black masculinity in a racially hegemonic society, the terror and racial cleansing in early twentieth-century Arkansas, the fear of drug-addicted Vietnam War veterans, the creation 

Historicizing Fear | Boyce Travis D. | Twarda

A detailed treatment of Mackey functors and homotopical applications in the broader context of enriched diagram categories, suitable for graduate students or researchers with an interest in category theory, equivariant homotopy theory, or related fields. A self-contained reference, with complete definitions and full proofs for non-expert readers.

Homotopy Theory of Enriched Mackey Functors | Johnson Niles | Ohio State University | Twarda

The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.This book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galo

Derived Langlands | Snaith Victor P. | Twarda

This is a book about the meanings of words and how they can combine to form larger meaningful units, as well as how they can fail to combine when the amalgamation of a predicate and argument would produce what the philosopher Gilbert Ryle called a 'category mistake'. It argues for a theory in which words get assigned both an intension and a type. The book develops a rich system of types and investigates its philosophical and formal implications, for example the abandonment of the classic Church analysis of types that has been used by linguists since Montague. The author integrates fascinating and puzzling observations about lexical meaning into a compositional semantic framework. Adjustments in types are a feature of the compositional process and account for various phenomena including coercion and copredication. This book will be of interest to semanticists, philosophers, logicians and computer scientists alike.

Lexical Meaning in Context | Asher Nicholas | Twarda

pThe Grothendieck construction provides an explicit link between indexed categories and opfibrations. It is a fundamental concept in category theory and related fields with far-reaching applications. Bipermutative categories are categorifications of rings. They play a central role in algebraic iKi-theory and infinite loop space theory.ppThis monograph is a detailed study of the Grothendieck construction over a bipermutative category in the context of categorically enriched multicategories, with new and important applications to inverse iKi-theory and pseudo symmetric iEi8734-algebras. After carefully recalling preliminaries in enriched categories, bipermutative categories, and enriched multicategories, we show that the Grothendieck construction over a small tight bipermutative category is a pseudo symmetric Cat-multifunctor and generally not a Cat-multifunctor in the symmetric sense.ppPseudo symmetry of Cat-multifunctors is a new concept we introduce in this work.ppThe following featur

Grothendieck Construction of Bipermutative | Indexed Categories | Yau Donald | Twarda | Twarda

Galois Theories | Borceux Francis | Twarda | Twarda

pThis book focuses on Robert Rosen's contributions to relational system theory, which is the science of organization and function. This science was originally developed by Nicolas Rashevsky, and further developed by Rashevsky's student Robert Rosen, and continues to be developed by Rosen's student A. H. Louie amongst others. Due to its revolutionary character, it is often misunderstood, and to some, controversial. The formal and conceptual setting for Rosen's relational system theory is category theory. Rosen was the first to apply category theory to scientific problems, outside of pure mathematics, and the first to think about science from the point of view of category theory. To better understand the work of Rosen, this book provides an overview of his theory of modeling, complexity, anticipation, and organism. It presents the foundations of this science and the philosophical motivations behind it along with conceptual clarification and historical context in order to present Rosen's 

Robert Rosen and Relational System Theory | Lennox James Bryan | Twarda

In contemporary feminist theory, the problem of feminine subjectivity persistently appears and reappears as the site that grounds all discussion of feminism. In iFeminism and the Abyss of Freedom, i Linda M. G. Zerilli argues that the persistence of this subject-centered frame severely limits feminists' capacity to think imaginatively about the central problem of feminist theory and practice a politics concerned with freedom. pOffering both a discussion of feminism in its postmodern context and a critique of contemporary theory, Zerilli here challenges feminists to move away from a theory-based approach, which focuses on securing or contesting women as an analytic category of feminism, to one rooted in political action and judgment. She revisits the democratic problem of exclusion from participation in common affairs and elaborates a freedom-centered feminism as the political practice of beginning anew, world-building, and judging. pIn a series of case studies, Zerilli draws on the pol

Feminism and the Abyss of Freedom | Zerilli Linda M. G. | Paperback | Twarda

pThis collection of fresh essays on Suzanne Collins's epic trilogy spans multiple disciplines. The contributors probe the trilogy's meaning using theories grounded in historicism, feminism, humanism, queer theory, as well as cultural, political, and media studies. The essayists demonstrate diverse perspectives regarding Collins's novels but their works have three elements in common an appreciation of the trilogy as literature, a belief in its permanent value, and a need to share both appreciation and belief with fellow readers. The 21 essays that follow the context-setting introduction are grouped into four parts Part I History, Politics, Economics, and Culture, Part II Ethics, Aesthetics, and Identity, Part III Resistance, Surveillance, and Simulacra, and Part IV Thematic Parallels and Literary Traditions. A core bibliography of dystopian and postapocalyptic works is included, with emphasis on the young adult category--itself an increasingly crucial part of postmodern culture. Instruc

Of Bread, Blood and the Hunger Games | Pharr Mary F. | Twarda

Decolonizing Time Work, Leisure, and Freedom demonstrates the importance of time as a central category for political theory, providing not only a history of the fight for time through political, feminist, and critical theory, but also assessing this tradition in the context of the United States.

Decolonizing Time | Shippen N. | Twarda

At the intersection of physics, mathematics, and computer science, an exciting new field of study has formed, known as Topological Quantum. This research field examines the deep connections between the theory of knots, special types of subatomic particles known as anyons, certain phases of matter, and quantum computation. This book elucidates this nexus, drawing in topics ranging from quantum gravity to topology to experimental condensed matter physics. Topological quantum has increasingly been a focus point in the fields of condensed matter physics and quantum information over the last few decades, and the forefront of research now builds on the basic ideas presented in this book. The material is presented in a down-to-earth and entertaining way that is far less abstract than most of what is in the literature. While introducing the crucial concepts and placing them in context, the subject is presented without resort to the highly mathematical category theory that underlies the field. 

Topological Quantum | Simon | Twarda | Twarda

pThis book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.ppIn recent years there has been a fascinating development concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of 

Mathematical Principles of Topological and Geometric Data Analysis | Joharinad Parvaneh | Twarda | Twarda

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pHow can music withstand the death and destruction brought on by war Global conflicts of the 20th century fundamentally transformed not only national boundaries, power relations, and global economies, but also the arts and culture of every nation involved. An important, unacknowledged aspect of these conflicts is that they have unique musical soundtracks. iMusic in World War IIi explores how music and sound took on radically different dimensions in the United States and Europe before, during, and after World War II. Additionally, the collection examines the impact of radio and film as the disseminators of the war's musical soundtrack. Contributors contend that the European and American soundtrack of World War II was largely one of escapism rather than the lofty, solemn, heroic, and celebratory mode of war music in the past. Furthermore, they explore the variety of experiences of populations forced from their homes and interned in civilian and POW camps in Europe and the United States, 

Music in World War II | Potter Pamela M. | Twarda

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category theory in context