IJPAM: Volume 95, No. 1 (2014)
A GROUP: SOME CONSTRUCTIONS
Department of Mathematics and Statistics
University of Tolima
Abstract. In this paper we introduce the category -pAct of partial actions of a fixed group . The objects or -psets are the sets endowed with a partial action of on and the morphisms, or preferably -pmorphisms, are the maps preserving this action. As a special achievement, we extend several well-known constructions in the category -Act, of global actions of , to this new context. In particular, we characterize products, coproducts, equalizers and pullbacks for arbitrary -pmorphisms. We also characterize coequalizers and pushouts for strong -pmorphisms (category -fpAct). Last, we prove that the category -pAct is complete and the category -fpAct is cocomplete.
Received: January 13, 2014
AMS Subject Classification: 18A30, 20M30
Key Words and Phrases: global action, partial action, product, equalizer, pullback, complete category
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DOI: 10.12732/ijpam.v95i1.6 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 45 - 56