We describe actions, semidirect products and crossed modules in categories of monoids with operations. Moreover we characterize, in this context, the internal categories corresponding to crossed modules. Concrete examples in the cases of monoids, semirings and distributive lattices are given.
Semidirect products and crossed modules in monoids with operations / N. Martins-Ferreira, A. Montoli, M. Sobral. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 217:2(2013), pp. 334-347.
Semidirect products and crossed modules in monoids with operations
A. Montoli
;
2013
Abstract
We describe actions, semidirect products and crossed modules in categories of monoids with operations. Moreover we characterize, in this context, the internal categories corresponding to crossed modules. Concrete examples in the cases of monoids, semirings and distributive lattices are given.
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