Directions for the Long Exact Cohomology Sequence in Moore Categories

摘要

A new method for realizing the first and second order cohomology groups of an internal abelian group in a Barr-exact category was introduced by Bourn (Cahiers Topologie G,om Diff,rentielle Cat,g XL:297-316, 1999; J Pure Appl Algebra 168:133-146, 2002). The main role, in each level, is played by a direction functor. This approach can be generalized to any level n and produces a long exact cohomology sequence. By applying this method to Moore categories we show that they represent a good context for non-abelian cohomology, in particular for the Baer Extension Theory.