  We study a multivariate, non-linear Hawkes process $Z^N$ on the complete
graph with $N$ nodes. Each vertex is either excitatory (probability $p$) or
inhibitory (probability $1-p$). We take the mean-field limit of $Z^N$, leading
to a multivariate point process $\bar Z$. If $p\neq\tfrac12$, we rescale the
interaction intensity by $N$ and find that the limit intensity process solves a
deterministic convolution equation and all components of $\bar Z$ are
independent. In the critical case, $p=\tfrac12$, we rescale by $N^{1/2}$ and
obtain a limit intensity, which solves a stochastic convolution equation and
all components of $\bar Z$ are conditionally independent.
