Andrea Montoli: Obstruction theory in action accessible categories

The notion of action accessible category is useful because it allows an intrinsic construction of centers and centralizers. This fact is an important tool in order to generalize the Schreier-MacLane theorem on the existence of extensions with fixed abstract kernel to this class of categories. We will show that any abstract kernel k corresponds to an element in a certain cohomology group of order 2, and that there exists an extension with abstract kernel k if and only if this element is the zero.