  There is a well-known fact in Poisson geometry that reduction commutes with
integration (of the associated integrable Lie algebroid). This is also valid
for other types of geometries given by 2-dimensional closed forms. In this
manuscript we extend this type of result to the particular case of cosymplectic
groupoids, obtaining in particular the reduction of a central extension defined
by a 2-IM form and a 1-IM form.
