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This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

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This book is a thoroughly revised edition of a monograph that presents an approach to the design and implementation of sequential programming languages based on the relationship between lambda-calculus and category theory. The foundations of a new "categorical" combinatory logic are laid down. Compilation and evaluation techniques are investigated. A simple abstract machine, called the Categorical Abstract Machine, is presented: it has served as the core of the implementation of the language CAML, of the ML family, developed at INRIA-Roquencourt and Ecole Normale Superieure, and first released in 1987. The main characteristics of this approach are conceptual simplicity and compactness, with bearings on portability, efficiency, and correctness proofs. A mathematical semantics of sequentiality is proposed, in which "sequential algorithms" rather than functions are used to interpret procedures. The theoretical investigation has led to the development of a programming language, CDSO, in which basic and functional types are not differentiated. The evaluation framework is a demand-driven data flow network. The model of sequential algorithms is fully abstract with respect to this language: two procedures have the same denotation if and only if they have the same behaviour. Background on full abstraction is given. The new edition covers new results, and introduces new connections, as suggested by the following non-exhaustive fist of keywords: confluence properties of categorical combinators, explicit substitutions, control operations, linear logic, geometry of interaction, strong stability.

Proceedings of the L'Aquila Conference 1994

Statisticians and researchers will find Categorical Data Analysis Using SAS, Third Edition, by Maura Stokes, Charles Davis, and Gary Koch, to be a useful discussion of categorical data analysis techniques as well as an invaluable aid in applying these methods with SAS. Practical examples from a broad range of applications illustrate the use of the FREQ, LOGISTIC, GENMOD, NPAR1WAY, and CATMOD procedures in a variety of analyses. Topics discussed include assessing association in contingency tables and sets of tables, logistic regression and conditional logistic regression, weighted least squares modeling, repeated measurements analyses, loglinear models, generalized estimating equations, and bioassay analysis. The third edition updates the use of SAS/STAT software to SAS/STAT 12.1 and incorporates ODS Graphics. Many additional SAS statements and options are employed, and graphs such as effect plots, odds ratio plots, regression diagnostic plots, and agreement plots are discussed. The material has also been revised and reorganized to reflect the evolution of categorical data analysis strategies. Additional techniques include such topics as exact Poisson regression, partial proportional odds models, Newcombe confidence intervals, incidence density ratios, and so on.

Categorical Data Analysis describes the most important methods, offering a unified presentation of modeling using generalized linear models and emphasizing loglinear and logit modeling techniques. Contributions of noted statisticians (Pearson, Yule, Fisher, Neyman, Cochran), whose pioneering efforts set the pace for the evolution of modern methods, are examined as well. Special features of the book include: Coverage of methods for repeated measurement data, which have become increasingly important in biomedical applications Prescriptions for how ordinal variables should be treated differently than nominal variables Derivations of basic asymptotic and fixed-sample-size inferential methods Discussion of exact small sample procedures More than 40 examples of analyses of "real" data sets, including: aspirin use and heart disease; job satisfaction and income; seat belt use and injuries in auto accidents; and predicting outcomes of baseball games More than 400 exercises to facilitate interpretation and application of methods Categorical Data Analysis also contains an appendix that describes the use of computer software currently available for performing the analyses presented in the book. A comprehensive bibliography and notes and the end of each chapter round out the work, making it a complete, invaluable reference for statisticians, biostatisticians and professional researchers.

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How do we sort the objects, people, events, and ideas in the world into their proper categories so that we may experience and interact with them? This fundamental question about human--and animal--perception and cognition is the subject of Categorical Perception, a comprehensive survey of a wide range of important research findings on the subject. The volume brings together all known examples of categorical perception, from research on humans and animals, infants and adults, in all the sense modalities: hearing, seeing, and touch. The perceptual findings are then interpreted in terms of the available cognitive and neuroscientific theories of how categorical perception is accomplished by the brain. Research on elementary perceptual and psychophysical categories is then compared with work on higher order categories such as objects, patterns, and abstract concepts. The book proceeds to an integrative view of categorization in general by exploring the most thoroughly investigated case of categorical perception--speech perception.

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A classic exposition of Kant's ethical thought.

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Classification, as an object of recent anthropological scrutiny came to prominence during the 1960s, exemplified in the British (constructionist) tradition by the writings of Mary Douglas, and in the American ethno-semantics (cognitive) tradition by the likes of Harold Conklin and Brent Berlin. At the time, these approaches seemed by turns to contradict each other, or even to exist in parallel universes. However, over the last 30 years we have witnessed both a renewed interest in classification studies as well as a cross-fertilization of these once antagonistic approaches. These essays by one of leading scholars in this field bring together a body of influential and inter-linked work which attempts to bridge the divide between cultural and cognitive studies of classification, and which develops a more embedded and processual approach. In particular, the essays focus on people’s categorization of natural kinds as a means through which to obtain an understanding of how classifying behavior in general works, engaging with the ideas of both anthropologists and psychologists. The theoretical background is set out in an entirely new and substantial introduction, which also provides a comprehensive and systematic review of developments in cognitive and social anthropology since 1960 as these have impacted on classification studies. In short, it constitutes a useful and approachable introduction to its subject.

Statisticians and researchers will find Categorical Data Analysis Using SAS, Third Edition, by Maura Stokes, Charles Davis, and Gary Koch, to be a useful discussion of categorical data analysis techniques as well as an invaluable aid in applying these methods with SAS. Practical examples from a broad range of applications illustrate the use of the FREQ, LOGISTIC, GENMOD, NPAR1WAY, and CATMOD procedures in a variety of analyses. Topics discussed include assessing association in contingency tables and sets of tables, logistic regression and conditional logistic regression, weighted least squares modeling, repeated measurements analyses, loglinear models, generalized estimating equations, and bioassay analysis. The third edition updates the use of SAS/STAT software to SAS/STAT 12.1 and incorporates ODS Graphics. Many additional SAS statements and options are employed, and graphs such as effect plots, odds ratio plots, regression diagnostic plots, and agreement plots are discussed. The material has also been revised and reorganized to reflect the evolution of categorical data analysis strategies. Additional techniques include such topics as exact Poisson regression, partial proportional odds models, Newcombe confidence intervals, incidence density ratios, and so on.

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This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

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This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given.

The first edition of this text has sold over 19,600 copies. However, the use of statistical methods for categorical data has increased dramatically in recent years, particularly for applications in the biomedical and social sciences. A second edition of the introductory version of the book will suit it nicely. Wiley also published a second edition of Categorical Data Analysis, which is an advanced, more technical text, in 2003.  

A valuable new edition of a standard reference The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data. Adding to the value in the new edition is: · Illustrations of the use of R software to perform all the analyses in the book · A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis · New sections in many chapters introducing the Bayesian approach for the methods of that chapter · More than 70 analyses of data sets to illustrate application of the methods, and about 200 exercises, many containing other data sets · An appendix showing how to use SAS, Stata, and SPSS, and an appendix with short solutions to most odd-numbered exercises Written in an applied, nontechnical style, this book illustrates the methods using a wide variety of real data, including medical clinical trials, environmental questions, drug use by teenagers, horseshoe crab mating, basketball shooting, correlates of happiness, and much more. An Introduction to Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and biostatisticians as well as methodologists in the social and behavioral sciences, medicine and public health, marketing, education, and the biological and agricultural sciences.