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Categories and sheaves
Autor: Kashiwara Masaki
Rok: c2006
ISBN: 9783540279495
OCLC Number: (OCoLC)61703264
OCLC Number: (ocolc)61703264
OKCZID: 110068088
Citace (dle ČSN ISO 690):
KASHIWARA, Masaki. Categories and sheaves. New York: Springer, c2006. x, 497 s. Grundlehren der mathematischen Wissenschaften. A series of comprehensive studies in mathematics, 332.
Hodnocení:
4.0 / 5
(6 hlasů)
Anotace
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.