Artículo
Abstract:
It is well known that the category of covering projections (that is, locally constant objects) of a locally connected topos is equivalent to the classifying topos of a strict progroupoid (or, equivalently, a localic prodiscrete groupoid), the fundamental progroupoid, and that this progroupoid represents first degree cohomology. In this paper we generalize these results to an arbitrary topos. The fundamental progroupoid is now a localic progroupoid, and cannot be replaced by a localic groupoid. The classifying topos is no longer a Galois topos. Not all locally constant objects can be considered as covering projections. The key contribution of this paper is a novel definition of covering projection for a general topos, which coincides with the usual definition when the topos is locally connected. The results in this paper were presented in a talk at the Category Theory Conference, Vancouver, July 2004. © 2008 Elsevier B.V. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | The fundamental progroupoid of a general topos |
| Autor: | Dubuc, E.J. |
| Filiación: | Departmento de Mathematica, Universidad de Buenos Aires, Pabellion 1 - Ciudad Universitaria, 1428 Buenos Aires, Argentina |
| Año: | 2008 |
| Volumen: | 212 |
| Número: | 11 |
| Página de inicio: | 2479 |
| Página de fin: | 2492 |
| DOI: | http://dx.doi.org/10.1016/j.jpaa.2008.03.022 |
| Título revista: | Journal of Pure and Applied Algebra |
| Título revista abreviado: | J. Pure Appl. Algebra |
| ISSN: | 00224049 |
| CODEN: | JPAAA |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v212_n11_p2479_Dubuc |
Referencias:
- Artin, M., Grothendieck, A., Verdier, J., (1972) Springer Lecture Notes in Mathematics, 269. , p. 270, 305
- Artin, M., Mazur, B., (1969) Springer Lecture Notes in Mathematics, 100
- Bunge, M., Classifying toposes and fundamental localic groupoids (1992) Category Theory '91, CMS Conf. Proc., 13. , Seely R.A.G. (Ed)
- Bunge, M., Moerdijk, I., On the construction of the Grothendieck fundamental group of a topos by paths (1997) J. Pure Appl. Algebra, 116
- Dubuc, E.J., (2003) Advances in Mathematics, 175-1, pp. 144-167
- Dubuc, E.J., On the representation theory of Galois and atomic topoi (2004) J. Pure Appl. Algebra, 186, pp. 233-275
- Grothendieck, A., (1971) Springer Lecture Notes in Mathematics, 224
- Hernandez-Paricio, L.J., Fundamental pro-groupoids and covering projections (1998) Fund. Math., 156
- Johnstone, P.T., (1977) Topos Theory, , Academic Press
- Joyal, A., Tierney, M., (1984) Memoirs of the American Mathematical Society, 151
- Kennison, J., The fundamental localic groupoid of a topos (1992) J. Pure Appl. Algebra, 77
- Mac Lane, S., Moerdijk, I., (1992) Sheaves in Geometry and Logic, , Springer Verlag
- Moerdijk, I., Continuous fibrations and inverse limits of toposes (1986) Compositio Math., 58
- Moerdijk, I., The classifying topos of a continuous groupoid (1988) Trans. Amer. Math. Soc., 310 (2)
- Moerdijk, I., Prodiscrete groups and Galois toposes (1989) Proc. Kon. Nederl. Akad. van Wetens. Series A, 92 (2)
- M. Tierney, Unpublished lecture at Columbia University, New York; Spanier, E.H., (1990) Algebraic Topology. second Springer printing, , Springer
Citas:
---------- APA ----------
(2008) . The fundamental progroupoid of a general topos. Journal of Pure and Applied Algebra, 212(11), 2479-2492.http://dx.doi.org/10.1016/j.jpaa.2008.03.022
---------- CHICAGO ----------
Dubuc, E.J. "The fundamental progroupoid of a general topos" . Journal of Pure and Applied Algebra 212, no. 11 (2008) : 2479-2492.http://dx.doi.org/10.1016/j.jpaa.2008.03.022
---------- MLA ----------
Dubuc, E.J. "The fundamental progroupoid of a general topos" . Journal of Pure and Applied Algebra, vol. 212, no. 11, 2008, pp. 2479-2492.http://dx.doi.org/10.1016/j.jpaa.2008.03.022
---------- VANCOUVER ----------
Dubuc, E.J. The fundamental progroupoid of a general topos. J. Pure Appl. Algebra. 2008;212(11):2479-2492.http://dx.doi.org/10.1016/j.jpaa.2008.03.022
