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Título
Baer Invariants and Cohomology of Precrossed Modules
Autor
Facultad/Centro
Área de conocimiento
Título de la revista
Applied Categorical Structures
Número de la revista
1
Datos de la obra
Arias, D. and Ladra, M. (2014). Baer Invariants and Cohomology of Precrossed Modules. Applied Categorical Structures, 22, 289–304. https://doi.org/10.1007/s10485-013-9307-x
Editor
Springer
Fecha
2014
ISSN
0927-2852
Résumé
[EN] In this paper we study Baer invariants of precrossed modules relative to the subcategory of crossed modules, following Fröhlich and Furtado-Coelho's general theory on Baer invariants in varieties of Ω-groups and Modi's theory on higher dimensional Baer invariants. Several homological invariants of precrossed and crossed modules were de fined in the last two decades. We show how to use Baer invariants in order to connect these various homology theories. First, we express the low-dimensional Baer invariants of precrossed modules in terms of a new non-abelian tensor product of a precrossed module. This expression is used to analyze the connection between the Baer invariants and the homological invariants of precrossed modules de ned by Conduché and Ellis. Specifi cally we prove that the second homological invariant of Conduché and Ellis is in general a quotient of the first component of the Baer invariant we consider. The defi nition of classical Baer invariants is generalized using homological methods. These generalized Baer invariants of precrossed modules are applied to the construction of fi ve term exact sequences connecting the generalized Baer invariants with the cohomology theory of crossed modules considered by Carrasco, Cegarra and R.-Grandjeán and the cohomology theory of precrossed modules.
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Palabras clave
Peer review
SI
ID proyecto
- MTM2009-14464-C02-01
- Incite09 207 215 PR
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