Categories and Sheaves

Masaki Kashiwara Professor at the Rims, Kyoto University Plenary speaker ICM 1978 Invited speaker ICM 1990 http://www.kurims.kyoto-u.ac.jp/~kenkyubu/kashiwara/ Pierre Schapira, Professor at University Pierre et Marie Curie (Paris VI) Invited speaker ICM 1990 http://www.math.jussieu.fr/~schapira/

• 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.

From the reviews: "This book of Kashiwara and Schapira, recognized specialists in algebraic analysis, is a detailed full-scale exposition of categories, homological algebra and sheaves. These notions are presented from scratch up to the most recent (sometimes new) results ... ." (Corrado Marastoni, Mathematical Reviews, Issue 2006 k)