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Proceedings of the American Mathematical Society

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Full and convex linear subcategories are incompressible

Authors: Claude Cibils, Maria Julia Redondo and Andrea Solotar
Journal: Proc. Amer. Math. Soc. 141 (2013), 1939-1946
MSC (2010): Primary 16W50, 18G55, 55Q05, 16B50
Published electronically: January 7, 2013
MathSciNet review: 3034421
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Abstract: Consider the intrinsic fundamental group à la Grothendieck of a linear category, introduced in our earlier papers using connected gradings. In this article we prove that any full convex subcategory is incompressible, in the sense that the group map between the corresponding fundamental groups is injective. We start by proving the functoriality of the intrinsic fundamental group with respect to full subcategories, based on the study of the restriction of connected gradings.

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Claude Cibils
Affiliation: Institut de mathématiques et de modélisation de Montpellier I3M, UMR 5149, Université Montpellier 2, F-34095 Montpellier cedex 5, France
MR Author ID: 49360
ORCID: 0000-0003-3269-9525

Maria Julia Redondo
Affiliation: Departamento de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca, Argentina
ORCID: 0000-0003-0857-3666

Andrea Solotar
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Instituto de Matemática Luis Santaló, IMAS-CONICET, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina
MR Author ID: 283990

Received by editor(s): July 15, 2010
Received by editor(s) in revised form: August 13, 2011, and September 27, 2011
Published electronically: January 7, 2013
Additional Notes: This work has been supported by the projects UBACYTX212 and 475, PIP-CONICET 112- 200801-00487, PICT-2007-02182 and MATHAMSUD-NOCOMALRET
The second and third authors are research members of CONICET (Argentina)
The authors thank the referee for useful comments
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2013 American Mathematical Society