Emily Riehl's Books

Categorical Homotopy Theory

By: Emily Riehl

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Categorical Homotopy Theory

By: Emily Riehl

This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.

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371

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Cambridge University Press

Published Date

ISBN 10

1107048451

ISBN 13

9781107048454

Category Theory in Context

By: Emily Riehl

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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.

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273

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Courier Dover Publications

Published Date

ISBN 10

0486820807

ISBN 13

9780486820804

Category Theory in Context

By: Emily Riehl

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Category Theory in Context

By: Emily Riehl

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. 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 range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. Prerequisites are limited to familiarity with some basic set theory and logic.

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273

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Courier Dover Publications

Published Date

ISBN 10

048680903X

ISBN 13

9780486809038

Elements of ∞-Category Theory

By: Emily Riehl,Dominic Verity

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Elements of ∞-Category Theory

By: Emily Riehl,Dominic Verity

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.

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Page Count

782

Publisher

Cambridge University Press

Published Date

ISBN 10

1108952194

ISBN 13

9781108952194

Categorical Homotopy Theory

By: Emily Riehl

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Categorical Homotopy Theory

By: Emily Riehl

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. Emily 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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371

Publisher

Cambridge University Press

Published Date

ISBN 10

1139952633

ISBN 13

9781139952637

Fat Chance

Probability from 0 to 1

By: Benedict Gross,Joe Harris,Emily Riehl

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Fat Chance

Probability from 0 to 1

By: Benedict Gross,Joe Harris,Emily Riehl

In a world where we are constantly being asked to make decisions based on incomplete information, facility with basic probability is an essential skill. This book provides a solid foundation in basic probability theory designed for intellectually curious readers and those new to the subject. Through its conversational tone and careful pacing of mathematical development, the book balances a charming style with informative discussion. This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Pair this book with the HarvardX online course for great videos and interactive learning: https://harvardx.link/fat-chance.

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Page Count

213

Publisher

Cambridge University Press

Published Date

ISBN 10

1108641822

ISBN 13

9781108641821

Reading Smell in Eighteenth-Century Fiction

By: Emily C. Friedman

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Reading Smell in Eighteenth-Century Fiction

By: Emily C. Friedman

Scent is both an essential and seemingly impossible-to-recover aspect of material culture. Scent is one of our strongest ties to memory, yet to remember a smell without external stimuli is almost impossible for most people. Moreover, human beings’ (specifically Western humans) ability to smell has been diminished through a process of increased emphasis on odor-removal, hygienic practices that emphasize de-odorization (rather than the covering of one odor by another).While other intangibles of the human experience have been placed into the context of the eighteenth-century novel, scent has so far remained largely sidelined in favor of discussions of the visual, the aural, touch, and taste. The past decade has seen a great expansion of our understanding of how smell works physiologically, psychologically, and culturally, and there is no better moment than now to attempt to recover the traces of olfactory perceptions, descriptions, and assumptions. Reading Smell provides models for how to incorporate olfactory knowledge into new readings of the literary form central to our understanding of the eighteenth century and modernity in general: the novel. The multiplication and development of the novel overlaps strikingly with changes in personal and private hygienic practices that would alter the culture’s relationship to smell. This book examines how far the novel can be understood through a reintroduction of olfactory information. After decades of reading for all kinds of racial, cultural, gendered, and other sorts of absences back into the novel, this book takes one step further: to consider how the recovery of forgotten or overlooked olfactory assumptions might reshape our understanding of these texts. Reading Smell includes wide-scale research and focused case studies of some of the most striking or prevalent uses of olfactory language in eighteenth-century British prose fiction. Highlighting scents with shifting meanings across the period: bodies, tobacco, smelling-bottles, and sulfur, Reading Smell not only provides new insights into canonical works by authors like Swift, Smollett, Richardson, Burney, Austen, and Lewis, but also sheds new light on the history of the British novel as a whole.

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Page Count

209

Publisher

Bucknell University Press

Published Date

ISBN 10

1611487536

ISBN 13

9781611487534

Fat Chance

Probability from 0 to 1

By: Benedict Gross,Joe Harris,Emily Riehl

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Fat Chance

Probability from 0 to 1

By: Benedict Gross,Joe Harris,Emily Riehl

Designed for the intellectually curious, this book provides a solid foundation in basic probability theory in a charming style, without technical jargon. This text will immerse the reader in a mathematical view of the world, and teach them techniques to solve real-world problems both inside and outside the casino.

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Page Count

213

Publisher

Cambridge University Press

Published Date

ISBN 10

1108482961

ISBN 13

9781108482967

Elements of ∞-Category Theory

By: Emily Riehl,Dominic Verity

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Elements of ∞-Category Theory

By: Emily Riehl,Dominic Verity

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Solve jigsaw puzzle

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Page Count

782

Publisher

Cambridge University Press

Published Date

ISBN 10

1108952194

ISBN 13

9781108952194

Book's by Emily Riehl

Categorical Homotopy Theory

Categorical Homotopy Theory

Category Theory in Context

Category Theory in Context

Category Theory in Context

Category Theory in Context

Elements of ∞-Category Theory

Elements of ∞-Category Theory

Categorical Homotopy Theory

Categorical Homotopy Theory

Fat Chance

Fat Chance

Reading Smell in Eighteenth-Century Fiction

Reading Smell in Eighteenth-Century Fiction

Fat Chance

Fat Chance

Elements of ∞-Category Theory

Elements of ∞-Category Theory

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