Geodesic
Crossed products of crossed modules of Hopf monoids
Theory and applications of categories, Tome 33 (2018), pp. 868-897.

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In this paper we consider a crossed product of two crossed modules of Hopf monoids in a strict symmetric monoidal category ${\mathcal C}$ and give necessary and sufficient conditions to get a new crossed module of Hopf monoids in ${\mathcal C}$. Moreover we introduce the notion of projection of crossed modules of Hopf monoids and show that with additional hypotheses, any of these projections defines a new crossed module of Hopf monoids and allows us to construct an example of this kind of crossed product. Finally, we develop the explicit computations of a crossed product associated to a projection of crossed modules in groups.
Publié le :
Classification : 18D10, 16W30, 16S40
Keywords: Hopf monoid, crossed module, entwining structure 
@article{TAC_2018_33_a28,
     author = {J.N. Alonso Alvarez and J.M. Fernandez Vilaboa and R. Gonzalez Rodriguez},
     title = {Crossed products of crossed modules of {Hopf} monoids},
     journal = {Theory and applications of categories},
     pages = {868--897},
     publisher = {mathdoc},
     volume = {33},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a28/}
}
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J.N. Alonso Alvarez; J.M. Fernandez Vilaboa; R. Gonzalez Rodriguez. Crossed products of crossed modules of Hopf monoids. Theory and applications of categories, Tome 33 (2018), pp. 868-897. http://geodesic.mathdoc.fr/item/TAC_2018_33_a28/