Duskin introduced his nerve functor (see the nLab or Kerodon) in the paper
Duskin, John W. Simplicial matrices and the nerves of weak n-categories I: nerves of bicategories. [Link].
While three other sequel papers were announced as "to appear", they never did. On the other hand, some papers (e.g. [1], [2]) cite drafts/preprints of the second part of Duskin's work. Is it available somewhere?