Handbook of Categorical Algebra: Volume 1, Basic Category Theory Borceux

Handbook of Categorical Algebra: Volume 1, Basic Category Theory

First of a 3-volume work giving a detailed account of what should be known by all working in, or using category theory. Volume 1 covers basic concepts.

Francis Borceux (Author)

9780521061193, Cambridge University Press

Paperback / softback, published 24 April 2008

364 pages
23.4 x 15.5 x 1.8 cm, 0.516 kg

"...these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical Reviews

A Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various 'refinements' of the fundamental concepts of category and functor.

Introduction1. The language of categories2. Limits3. Adjoint functors4. Generators and projectives5. Categories of fractions6. Flat functors and Cauchy completeness7. Bicategories and distributors8. Internal category theoryBibliographyIndex.

Subject Areas: Mathematical foundations [PBC]