Categories and Sheaves (Grundlehren der mathematischen Wissenschaften)
Edition: 1 edition
Publisher: Springer
Published: December 1, 2005
Language: eng
Format: Hardcover
Number of pages: 497
ISBN-13: 9783540279495
Subjects: Algebra; Mathematics; Science/Mathematics; Algebra - General; Geometry - General; Category theory; Mathematics / Algebra / General; homological algebra; sheaves; stacks; unbound derived categories
Description: Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays. This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies.