Korean J. Math. Vol. 27 No. 2 (2019) pp.535-545
DOI: https://doi.org/10.11568/kjm.2019.27.2.535

Crossed semimodules and cat$^{\bf 1}$-monoids

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Published: Jun 30, 2019
Keywords:
Crossed module, crossed semimodule, cat$^1$-group, cat$^1$-monoid
Mathematics Subject Classification:
20L05, 18D05, 18D35, 20J15

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Sedat Temel
Department of Mathematics Recep Tayyip Erdogan University, Rize, Turkey

Abstract

The main idea of this paper is to introduce the notion of cat$^{\bf{1}}$-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$^{\bf{1}}$-monoids. This is a generalization of the well known equivalence between category of cat$^{\bf{1}}$-groups and that of crossed modules over groups.


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