Inonu University, Science and Art Faculty, Department of Mathematics
Abstract
In this work we deal with actions of vector groupoid which is a new concept in the literature. After we give the definition of the action of a vector groupoid on a vector space, we obtain some results related to actions of vector groupoids. We also apply some characterizations of the category and groupoid theory to vector groupoids. As the second part of the work, we define the notion of a crossed module over a vector groupoid. Finally, we show that the category $mathcal{VG}$ of the vector groupoids is equivalent to the category $mathcal{CM}odmathcal{VG}$ of the crossed modules over a vector groupoid.
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