Unbounded Algebraic Derivators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910448574529536 |
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| author | Alonso, Leovigildo Álvarez, Beatriz Jeremías, Ana |
| author_facet | Alonso, Leovigildo Álvarez, Beatriz Jeremías, Ana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05918 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Unbounded Algebraic Derivators Alonso, Leovigildo Álvarez, Beatriz Jeremías, Ana Category Theory Algebraic Geometry Representation Theory 18G80 (primary), 18G35, 13D45, 20J06 (secondary) 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. |
| title | Unbounded Algebraic Derivators |
| topic | Category Theory Algebraic Geometry Representation Theory 18G80 (primary), 18G35, 13D45, 20J06 (secondary) |
| url | https://arxiv.org/abs/2111.05918 |