Category Theory in Context

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Courier Dover Publications, 16 nov. 2016 - 272 pages

 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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Table des matières

Categories Functors Natural Transformations
1
Universal Properties Representability and the Yoneda Lemma
49
Limits and Colimits
73
Adjunctions
115
Monads and their Algebras
153
All Concepts are Kan Extensions
189
Theorems in Category Theory
217
Bibliography
225
Glossary of Notation
231
193
239
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À propos de l'auteur (2016)

Emily Riehl is Assistant Professor in the Department of Mathematics at Johns Hopkins University. She received her Ph.D. from the University of Chicago in 2011 and was a Benjamin Pierce and NSF Postdoctoral Fellow at Harvard University from 2011-15. She is also the author of Categorical Homotopy Theory.

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