league vs unify

league is a noun but unify is not a noun.

Word	Noun	Adjective	Verb	Adverb
league	Yes	No	Yes	No
unify	No	No	Yes	No

As verbs, unify is a hypernym of league; that is, unify is a word with a broader meaning than league:

Other hypernyms of league include unite.

league (noun)	unify (noun)
an association of states or organizations or individuals for common action
an association of sports teams that organizes matches for its members
an obsolete unit of distance of variable length (usually 3 miles)

league (verb)	unify (verb)
unite to form a league	become one
	join or combine
	to bring or combine together or with something else
	act in concert or unite in a common purpose or belief
	bring together for a common purpose or action or ideology or in a shared situation