Representation cohomology is the cohomology of the cochain complex obtained from Grothendieck groups of kC_n-modules for the simplicial category whose level-n objects are the simplices of the nerve of a small category C.
Xu,Representations of categories and their applications, Journal of Algebra, 317 pp
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Representation Cohomology of a Small Category
Representation cohomology is the cohomology of the cochain complex obtained from Grothendieck groups of kC_n-modules for the simplicial category whose level-n objects are the simplices of the nerve of a small category C.