Reduction of Cosymplectic Groupoids

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.