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.
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