What is it called when a country's laws apply to its citizens outside the country?

Question

Suppose that a European country X (e.g. Germany) has a law against adults sleeping with people under the age of 16. Such a law, in this instance, would apply to anyone in German territory.

But suppose the law was that a German citizen isn't allowed to go to Asian country Y, where sleeping with 15 year olds is legal, and do in that country what is illegal under German law in Germany.

What is that called? The term I was thinking of was "extraterritoriality," but I was told that was a situation where the German was exempt from the law of the Asian country, e.g. China in the early 20th century.

Answer 1

You are looking for extraterritorial jurisdiction:

As the term indicates, it connotes the exercise of jurisdiction, or legal power, outside territorial borders.

This can include nations claiming jurisdiction over crimes in nearby bodies of water and to specific categories of crimes (such as sexual offenses against underage victims) committed by or against citizens while abroad.

Wikipedia has a summary, including a few different nations' application of extraterritorial jurisdiction. The Cornell Law Review has a very extensive essay, What is Extraterritorial Jurisdiction?

Answer 2

In this specific situation, the law in question is criminal law, so the term you are looking for is the principle of personality.

This is usually codified alongside the principle of territoriality (which you mention in the first paragraph), the protective principle and the principle of universality. All of this applies to criminal law only.