We extend some properties of pullbacks which are known to hold in a Mal'tsev
context to the more general context of Gumm categories. The varieties of
universal algebras which are Gumm categories are precisely the congruence
modular ones. These properties lead to a simple alternative proof of the known
property that central extensions and normal extensions coincide for any Galois
structure associated with a Birkhoff subcategory of an exact Goursat category.Comment: 12 page
