Before revision:  I show that the weights on some conditional LATEs are negative and the IV estimand is no longer interpretable as a causal effect under conditional monotonicity, i.e. when there are compliers but no defiers at some covariate values and defiers but no compliers elsewhere.
After revision:  I show that the weights on some conditional LATEs are negative and the IV estimand is no longer interpretable as a causal effect under a weaker version of monotonicity, i.e. when there are compliers but no defiers at some covariate values and defiers but no compliers elsewhere.