It's not what you think. Or hope.
A copulative verb is a verb form that joins a subject to an adjective or to another noun. The verb to be is a copulative verb. So are the linking verbs (seem, appear, look, become, and others).
The verb to be may join a subject to a noun or an adjective. Study these two examples:
John is my friend. (noun)
John is happy. (adjective)