....to get an overview you may start checking the review published by Barthod et al 2018: Article Composting with additives to improve organic amendments. A review
@ Christian, may be because all processes in the nitrogen cycle co-exist simultaneously during composting, including ammonification, nitrification, denitrification, nitrogen fixation and so on. But the fixation of N is depends upon the C:N ratio of the compost which is definitely best at 30:1. It has also been found that during composting, some of the organic N was slowly converted to the much smaller inorganic N pools. The mineralization process was continued further by conversion of ammonium to nitrite/nitrate by nitrifiers.
Yes, for a short time there is a N-Fixation because there is sudden increase in microbial population and they use available Soil Nitrogen as their food source until the compost N not available. You may called it as a short term "Soil depression".