TY  - BOOK
AU  - Kashiwara,Masaki
AU  - Schapira,Pierre
ED  - SpringerLink (Online service)
TI  - Categories and Sheaves
T2  - Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
SN  - 9783540279501
AV  - QA169 
U1  - 512.6 23
PY  - 2006///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Category theory (Mathematics)
KW  - Homological algebra
KW  - Manifolds (Mathematics)
KW  - Complex manifolds
KW  - Category Theory, Homological Algebra
KW  - Manifolds and Cell Complexes (incl. Diff.Topology)
KW  - Electronic books
KW  - local
N1  - The Language of Categories -- Limits -- Filtrant Limits -- Tensor Categories -- Generators and Representability -- Indization of Categories -- Localization -- Additive and Abelian Categories -- ?-accessible Objects and F-injective Objects -- Triangulated Categories -- Complexes in Additive Categories -- Complexes in Abelian Categories -- Derived Categories -- Unbounded Derived Categories -- Indization and Derivation of Abelian Categories -- Grothendieck Topologies -- Sheaves on Grothendieck Topologies -- Abelian Sheaves -- Stacks and Twisted Sheaves
N2  - 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
UR  - http://ezproxy.alfaisal.edu/login?url=http://dx.doi.org/10.1007/3-540-27950-4
ER  -