Geodesic
A note on internal object action representability of 1-cat groups and crossed modules
Theory and applications of categories, Tome 34 (2019), pp. 1165-1178

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The category of 1-cat groups, which is equivalent to the category of crossed modules, has internal object actions which are representable (by internal automorphism groups). Moreover, it is known that the crossed module, corresponding to the representing object [X] = Aut(X) $ associated with a 1-cat group X, must be isomorphic to the Norrie actor of the crossed module corresponding to X. We recall the description of Aut(X) from the author's PhD thesis, and construct that isomorphism explicitly.

Publié le :
Classification : 18G55, 18D15, 18D05, 20L05
Keywords: crossed module, action of an object, $ 1 $-cat group, internal automorphism, actor 
@article{TAC_2019_34_a35,
     author = {Pako Ramasu},
     title = {A note on internal object action representability of 1-cat groups and 
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     journal = {Theory and applications of categories},
     pages = {1165--1178},
     publisher = {mathdoc},
     volume = {34},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a35/}
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Pako Ramasu. A note on internal object action representability of 1-cat groups and 
crossed modules. Theory and applications of categories, Tome 34 (2019), pp. 1165-1178. http://geodesic.mathdoc.fr/item/TAC_2019_34_a35/