# Actions of vector groupoids

Document Type : Research Paper

Author

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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### History

• Receive Date: 25 December 2012
• Revise Date: 18 April 2013
• Accept Date: 18 April 2013