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arXiv · 2111.05918

Unbounded Algebraic Derivators

Leovigildo Alonso·Beatriz Álvarez·Ana Jeremías
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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.

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Leovigildo Alonso, Beatriz Álvarez, Ana Jeremías. 2023-09-14. Unbounded Algebraic Derivators. https://doi.org/10.1007/s10485-023-09752-x

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