Saunders Mac Lane
Categories for the working mathematician - 2nd ed. - New York: Springer, [c1998] - 262 p - Graduate Texts in Mathematics .
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
9780387984032
QA169
Categories for the working mathematician - 2nd ed. - New York: Springer, [c1998] - 262 p - Graduate Texts in Mathematics .
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
9780387984032
QA169