Cambridge Studies in Advanced Mathematics #: Elements of Category Theory

Cambridge Studies in Advanced Mathematics #: Elements of Category Theory
Emily Riehl, Dominic Verity
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Hardback
h234 x 155mm - 770pg
10 Feb 2022 UK
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9781108837989
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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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' Emily and Dom have done what many thought impossible: they have written an introductory text on a model-independent approach to higher category theory. This self-contained text is ideal for both end-users and architects of higher category theory. Every page is bursting at the seams with gorgeous insights and the refreshingly candid delight the authors take in their subject. ' Clark Barwick, University of Edinburgh ' This remarkable book starts with the premise that it should be possible to study infinity-categories armed only with the tools of 2-category theory. It is the result of the authors' decade-long collaboration, and they have poured into it all their experience, technical brilliance, and expository skill. I' m sure I' ll be turning to it for many years to come. ' Steve Lack, Macquarie University
Emily Riehl is an associate professor of mathematics at Johns Hopkins University. She received her PhD from the University of Chicago and was a Benjamin Peirce and NSF postdoctoral fellow at Harvard University. She is the author of Categorical Homotopy Theory (Cambridge, 2014) and Category Theory in Context (2016), and a co-author of Fat Chance: Probability from 0 to 1 (Cambridge, 2019). She and her present co-author have published ten articles over the course of the past decade that develop the new mathematics appearing in this book. Dominic Verity is a professor of mathematics at Macquarie University in Sydney and is a director of the Centre of Australian Category Theory. While he is a leading proponent of ' Australian-style' higher category theory, he received his PhD from the University of Cambridge and migrated to Australia in the early 1990s. Over the years he has pursued a career that has spanned the academic and non-academic worlds, working at times as a computer programmer, quantitative analyst, and investment banker. He has also served as the Chair of the Academic Senate of Macquarie University, the principal academic governance and policy body.
Status: Active
ISBN-13: 9781108837989
Published: 10 Feb 2022
Published In: United Kingdom
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Format: Hardback
Height: 234mm
Width: 155mm
Spine: 45mm
Weight: 1210g
Pages: 770

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