I was wondering what a good source for the properties (or even the existence) of the abelianisation of a (2-) groupoid would be? A naive construction would certainly be to abelianise the automorphisms (this is also mentioned here) but maybe that isn't the best construction?

As for basic properties I'm curious about: is this an exact (or rather $2$-exact) functor and adjoint to the inclusion-functor of groupoids into abelian groupoids (by which I should probably mean abelian objects in the category of categories?)