Legal Question in Criminal Law in California

It can go both ways. Is it lawful to tell someone why they're being detained? Absolutely. In fact, most officers will tell them why they're being detained and hopefully get some sort of statement from the individual.

Is it just as "lawful" for them to NOT tell the individual why they're being detained? Yes. For example, let's say the police are investigating a rape in the area. If they detain somebody for investigation, but don't tell them what crime they're investigating - if the suspect then says something that indicates they know what the crime is, it can be used against them. If they weren't involved, why else would they know what the crime was since the police didn't tell them? At least that's their argument.

The question started with "case law on arresting." For an arrest, that's different. If a person is arrested, the police must inform them why they're being arrested unless they were caught in the act.