What is the relationship between federalism and Federal and State court systems in the United States?

What is the relationship between federalism and federal and state court systems in the United States?

The video below provides a very short introduction to federalism.  Because of federalism, power is divided between the national government and state governments in the United States.  Some powers belong to the national government and some powers belong to the state governments.  Some powers are shared.

Because of federalism, each state in the United States has established its own court system.   But there is also a national court system, known as the federal court system.  The highest court in the federal court system is the Supreme Court of the United States.  Congress has also established inferior appellate level and trial level federal courts.