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The Intrinsic Fundamental Group of a Linear Category

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Abstract

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal covering. The grading deduced from a Galois covering enables us to describe the canonical monomorphism from its automorphism group to the first Hochschild-Mitchell cohomology vector space.

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Authors and Affiliations

  1. Institut de Mathématiques et de Modélisation de Montpellier I3M, UMR 5149, Université Montpellier 2, 34095, Montpellier cedex 5, France

    Claude Cibils

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

    María Julia Redondo

  3. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina

    Andrea Solotar

Authors
  1. Claude Cibils
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  2. María Julia Redondo
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  3. Andrea Solotar
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Corresponding author

Correspondence to Claude Cibils.

Additional information

This work has been supported by the projects MATHAMSUD, UBACYTX212, PIP-CONICET 112-2000801-00487 and PICT-2007-02182 (ANPCyT). The second and third authors are research members of CONICET (Argentina) and the third author is a Regular Associate of ICTP Associate Scheme.

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Cibils, C., Redondo, M.J. & Solotar, A. The Intrinsic Fundamental Group of a Linear Category. Algebr Represent Theor 15, 735–753 (2012). https://doi.org/10.1007/s10468-010-9263-1

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  • DOI: https://doi.org/10.1007/s10468-010-9263-1

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