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http://dx.doi.org/10.11568/kjm.2019.27.2.535

CROSSED SEMIMODULES AND CAT1-MONOIDS  

Temel, Sedat (Department of Mathematics Recep Tayyip Erdogan University)
Publication Information
Korean Journal of Mathematics / v.27, no.2, 2019 , pp. 535-545 More about this Journal
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.
Keywords
Crossed module; crossed semimodule; $cat^1$-group; $cat^1$-monoid;
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