Actions of H-module Groupoids

Abstract

Let H be a ring, 1H be the identity of ring H and N be an H-module on H. In this work, we are going to give a new definition that it is called an action of H-module groupoids. First, we are going to give the definition of the action of the H-module groupoids on the H-module N. Then we obtained a new category HMGpdOp(Ω) of actions of Ω on H-modules. We also find that there is a groupoid Ω x N on N. Ω x N is called the action H-module groupoid. Finally, we prove that the category HMGpdOp(Ω) of actions of H-module groupoids is equivalent to HMGpdCov(Ω) of coverings of H-module groupoids.