Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CROSSED SEMIMODULES AND CAT1-MONOIDS

  • Temel, Sedat (Department of Mathematics Recep Tayyip Erdogan University)
  • Received : 2019.02.07
  • Accepted : 2019.06.15
  • Published : 2019.06.30
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Abstract

The main idea of this paper is to introduce the notion of $cat^1$-monoids and to prove that the category of crossed semimodules ${\mathcal{C}}=(A,B,{\partial})$ where A is a group is equivalent to the category of $cat^1$-monoids. This is a generalization of the well known equivalence between category of $cat^1$-groups and that of crossed modules over groups.

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References

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