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  3. Basic Category Theory
  • Cited by 97
Publisher:
Cambridge University Press
Online publication date:
August 2014
Print publication year:
2014
Online ISBN:
9781107360068
DOI:
https://doi.org/10.1017/CBO9781107360068
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
Series:
Cambridge Studies in Advanced Mathematics (143)
Information

Book description

At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties all three together. The book is suitable for use in courses or for independent study. Assuming relatively little mathematical background, it is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations. Copious exercises are included.

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Contents

Contents
References
Further reading
Saunders Mac, Lane, Categories for the Working Mathematician. Springer, 1971; second edition with two new chapters, 1998.
Steve, Awodey, Category Theory. Oxford University Press, 2010.
Saunders Mac, Lane, Mathematics: Form and Function. Springer, 1986.
F. William, Lawvere and Stephen H., Schanuel, Conceptual Mathematics: A First Introduction to Categories. Cambridge University Press, 1997.
Francis, Borceux, Handbook of Categorical Algebra, Volumes 1-3. Cambridge University Press, 1994.
Various authors, The nLab. Available at http://ncatlab.org, 2008-present.
Timothy, Gowers, Mathematics: A Very Short Introduction. Oxford University Press, 2002.
G. M., Kelly, Basic Concepts of Enriched Category Theory. Cambridge University Press, 1982. Also Reprints in Theory and Applications of Categories 10 (2005), 1-136, available at www.tac.mta.ca/tac/reprints.
F. William, Lawvere and Robert, Rosebrugh, Sets for Mathematics. Cambridge University Press, 2003.
Tom, Leinster, Rethinking set theory. American Mathematical Monthly, to appear (2014). Also available at http://arxiv.org/abs/1212.6543.

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