Categories for the working mathematician

By: Saunders Mac LaneMaterial type: TextTextSeries: Graduate Texts in MathematicsPublication details: New York: Springer, [c1998]Edition: 2nd edDescription: 262 pISBN: 9780387984032LOC classification: QA169
Contents:
Introduction 1. Categories, Functors, and Natural Transformations 2. Constructions on Categories 3. Universals and Limits 4. Adjoints 5. Limits 6. Monads and Algebras 7. Monoids 8. MonoidsAbelian Categories 9. Special Limits 10. Kan Extensions 11. Symmetry and Braidings in Monoidal Categories 12. Structures in Categories
Summary: Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is onsymmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories. --- summary provided by publisher
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 4 QA169 (Browse shelf (Opens below)) Available Invoice no. IN 160 ; Date 22-04-2019 01999
Total holds: 0

Introduction
1. Categories, Functors, and Natural Transformations
2. Constructions on Categories
3. Universals and Limits
4. Adjoints
5. Limits
6. Monads and Algebras
7. Monoids
8. MonoidsAbelian Categories
9. Special Limits
10. Kan Extensions
11. Symmetry and Braidings in Monoidal Categories
12. Structures in Categories

Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is onsymmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories. --- summary provided by publisher

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