IJPAM: Volume 95, No. 1 (2014)
A GROUP: SOME CONSTRUCTIONS




University of Tolima
Ibagué, COLOMBIA
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
Year: 2014
Volume: 95
Issue: 1
Pages: 45 - 56
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This work is licensed under the Creative Commons Attribution International License (CC BY).