Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.
Segal,Classifying spaces and spectral sequences, Publ
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On formality of diagrams of Eilenberg-MacLane spaces
Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.