Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
- Includes diagrammatical proofs, examples and exercises to encourage an active way of learning
- Provides enough background from category theory to make advanced topics such as K-theory, iterated loop spaces and functor homology accessible to readers
- Makes abstract concepts tangible, encouraging readers to learn what can be an intimidating subject
Read more
Reviews & endorsements
'It would be an excellent text for a graduate student just finishing introductory coursework and wanting to know about techniques in modern homotopy theory.' Julie Bergner
'… this book attempts to bridge the gap between the basic theory and the application of categorical methods to homotopy theory, which has been the subject of some recent exciting developments … the book would be very useful for beginner graduate students in homotopy theory.' Hollis Williams, IMA website
'The book has been thoughtfully written with students in mind, and contains plenty of pointers to the literature for those who want to pursue a subject further. Readers will find themselves taken on an engaging journey by a true expert in the field, who brings to the material both insight and style.' Daniel Dugger, MathSciNet (https://mathscinet.ams.org)
See more reviews
Customer reviews

Not yet reviewed
Be the first to review

Log in to review

Review was not posted due to profanity
×

, create a review

(If you're not , sign out)

Please enter the right captcha value

Please enter a star rating.

Your review must be a minimum of 12 words.

How do you rate this item?

Reviews must contain at least 12 words about the product.

×

Product details
- Date Published: April 2020
- format: Hardback
- isbn: 9781108479622
- length: 400 pages
- dimensions: 235 x 156 x 26 mm
- weight: 0.68kg
- contains: 115 exercises
- availability: Available
Table of Contents
Introduction
Part I. Category Theory:
1. Basic notions in category theory
2. Natural transformations and the Yoneda lemma
3. Colimits and limits
4. Kan extensions
5. Comma categories and the Grothendieck construction
6. Monads and comonads
7. Abelian categories
8. Symmetric monoidal categories
9. Enriched categories
Part II. From Categories to Homotopy Theory:
10. Simplicial objects
11. The nerve and the classifying space of a small category
12. A brief introduction to operads
13. Classifying spaces of symmetric monoidal categories
14. Approaches to iterated loop spaces via diagram categories
15. Functor homology
16. Homology and cohomology of small categories
References
Index.
Look Inside

General Resources

Links

Find resources associated with this title

Back to resources home

Type	Name	Unlocked *	Format	Size

Showing of

This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

If you are having problems accessing these resources please contact [email protected].

Author
Birgit Richter, Universität Hamburg
Birgit Richter is Professor of Mathematics at Universität Hamburg. She is the co-editor of Structured Ring Spectra (2004) and New Topological Contexts for Galois Theory and Algebraic Geometry (2009).