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The Intrinsic Fundamental Group of a Linear Category |
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| Authors: | Claude Cibils María Julia Redondo Andrea Solotar |
| Institution: | 1. Institut de Mathématiques et de Modélisation de Montpellier I3M, UMR 5149, Université Montpellier 2, 34095, Montpellier cedex 5, France 2. Departamento de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000, Bahía Blanca, Argentina 3. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina |
| 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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