Directions for the long exact cohomology sequence in Moore categories (Q835750)

\textit{D. Bourn} [Cah. Topologie Géom. Différ. Catég. 40, No. 4, 297--316 (1999; Zbl 0988.18006) and J. Pure Appl. Algebra 168, No. 2--3, 133--146 (2002; Zbl 1015.18001)] presented a new method for realizing the first and second order cohomology groups of an internal abelian group in a Barr-exact category. In the paper under review it is explained that this approach can be generalized to any level and produces a long exact cohomology sequence. Using this approach, it is showed that Moore categories represent a good context for non-abelian cohomology.