By Koudenburg The paper (arXiv:[1511.04070])(https://arxiv.org/pdf/1511.04070) generalizes 2-monad associated to hyper virtual double category.
Another paper (arXiv:[1310.8279]) (https://arxiv.org/abs/1310.8279), by Emily, Dominic, gives a theory of $(\infty,1)$-monad.
May I have the references for monads on higher categories such as $\infty-$groupoid, $n$-category and $(n,r)$-category ?