IJPAM: Volume 95, No. 1 (2014)

THE CATEGORY OF PARTIAL ACTIONS OF
A GROUP: SOME CONSTRUCTIONS

Jesús Ávila$^1$, Soledad Buitrago$^2$, Sabrina Zapata$^3$
$^{1,2,3}$Department of Mathematics and Statistics
University of Tolima
Ibagué, COLOMBIA


Abstract. In this paper we introduce the category $G$-pAct of partial actions of a fixed group $G$. The objects or $G$-psets are the sets $X$ endowed with a partial action of $G$ on $X$ and the morphisms, or preferably $G$-pmorphisms, are the maps preserving this action. As a special achievement, we extend several well-known constructions in the category $G$-Act, of global actions of $G$, to this new context. In particular, we characterize products, coproducts, equalizers and pullbacks for arbitrary $G$-pmorphisms. We also characterize coequalizers and pushouts for strong $G$-pmorphisms (category $G$-fpAct). Last, we prove that the category $G$-pAct is complete and the category $G$-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
Year: 2014
Volume: 95
Issue: 1
Pages: 45 - 56


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