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Cohomology of the Grothendieck construction

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Abstract

We consider cohomology of small categories with coefficients in a natural system in the sense of Baues and Wirsching. For any functor L : K → CAT, we construct a spectral sequence abutting to the cohomology of the Grothendieck construction of L in terms of the cohomology of K and of L(k), for k ∈ ObK.

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Authors and Affiliations

  1. Razmadze Mathematical Institute of Georgian Academy of Sciences, Alexidze str. 1, Tbilisi, 0193, Republic of Georgia

    Teimuraz Pirashvili

  2. Instituto de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000, Bahía Blanca, Argentina

    Marí a Julia Redondo

Authors
  1. Teimuraz Pirashvili
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  2. Marí a Julia Redondo
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Correspondence to Teimuraz Pirashvili.

Additional information

The first author was supported by DFG at University of Bielefeld

The second author is a researcher from CONICET, Argentina

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Pirashvili, T., Julia Redondo, M. Cohomology of the Grothendieck construction. manuscripta math. 120, 151–162 (2006). https://doi.org/10.1007/s00229-006-0634-1

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  • DOI: https://doi.org/10.1007/s00229-006-0634-1

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