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Handbook of Categorical Algebra
Author(s): Francis Borceux
Series: Encyclopedia of mathematics and its applications 50-51, 53 [i.e. 52]
Publisher: Cambridge University Press, Year: 1994
ISBN: 0521441781
Book Description:
A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. 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.
Handbook of categorical algebra : 1 Basic Category Theory
Handbook of categorical algebra : 2 Categories and Structures
The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject’s development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou’s ideas of fibered categories.
Handbook of Categorical Algebra: 3 Sheaf Theory
This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given.
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