The equivalence between groupoids and crossed modules from a
categorical point of view, with application in the case of groups
Starting with the well known equivalence of internal groupoids and
crossed modules, in the case of groups, involving also the equivalence
between points and actions, and the adjunction between actions by
conjugation and semidirect products, we consider the problem of finding an
appropriate general setting, from a categorical point of view, and to give
some necessary and sufficient conditions, for the general case, in order to
have similar results as in the case of groups.
For that purpose we introduce concepts as "abstract actions",
"semidirect-product diagrams" or "abstract crossed modules".
Nelson Martins-Ferreira (CDRSP/IPLeiria)
September 22, 2009