Is this a mistake? (regarding maximum likelihood estimator)

Under 'general remarks' on maximum likelihood estimators. I don't understand the right hand side of ii. (it is also repeated in iii. this time as the log-likelihood function). That the MLE is theta hat equals arg-theta-max makes sense but why does the likelihood function of theta hat also equal arg-theta-max? Doesn't this imply that theta-hat equals its own likelihood function? This doesn't make sense to me. Should it?

I believe the second parts should read $$L(\hat{\theta}) = \max_{\theta} L(\theta)$$ and $$l(\hat{\theta}) = \max_{\theta} l(\theta)$$