Unbounded Algebraic Derivators
arXiv:2111.05918 · doi:10.1007/s10485-023-09752-x
Abstract
We show that the unbounded derived category of a Grothendieck category with enough projective objects is the base category of a derivator whose category of diagrams is the full 2-category of small categories. With this structure, we give a description of the localization functor associated to a specialization closed subset of the spectrum of a commutative noetherian ring. In addition, using the derivator of modules, we prove some basic theorems of group cohomology for complexes of representations over an arbitrary base ring.
V3, final version, V2 Corrected proof of Proposition 2.10 and several other improvements. 32 pages