For small categories over a fixed object set, cohomology can be computed via direction functors on S-special morphisms, matching Hoff and Golasinski cohomology in every degree.
Golasi´ nski,n-fold extensions and cohomologies of small categories, Math´ ematica – Revue d’Analyse Num´ erique et de Th´ eorie de l’Approximation
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A direction functor approach to the cohomology of small categories
For small categories over a fixed object set, cohomology can be computed via direction functors on S-special morphisms, matching Hoff and Golasinski cohomology in every degree.