Copula

A linking verb whose main function is to relate other elements of clause structure, especially subject and complement, as in ‘the cup is on the table’, ‘these are hamsters’.  Thus, it is the verb of existence, such as the English verb ‘be’.  A zero copula, a feature of African-American English, Arabic, Hebrew, Hungarian and Russian, is when an overt copula like ‘is’ is omitted as in ‘He running’.  Children’s first sentences in English contain zero copulas.

See Grammaticization (or grammaticalization), Language development, Predicates (grammar), Syntax