nLab
internal crossed module

Crossed modules of groups, differential crossed modules, and crossed modules of crossed modules, are a special case of an (internal) crossed module in a semi-abelian category which is along with precrossed modules introduced in

• G. Janelidze, Internal crossed modules, Georgian Math. J. 10 (2003) 99114 (journal).

In Mal’cev categories there is an article on precrossed modules

• T. Everaerta, M. Gran, Precrossed modules and Galois theory, J. Algebra 297, no. 1 (2006) 292–309 doi:10.1016/j.jalgebra.2005.06.034.