  We show that the category of internal groupoids in an exact Mal'tsev category
is reflective, and in fact a Birkhoff subcategory of the category of simplicial
objects. We then characterize the central extensions of the corresponding
Galois structure, and show that regular epimorphisms admit a relative
monotone-light factorization system in the sense of Chikhladze. We also draw
some comparison with Kan complexes. By comparing the reflections of simplicial
objects and reflexive graphs into groupoids, we exhibit a connection with
weighted commutators (as defined by Gran, Janelidze and Ursini).
