A copula is a word which combines with a syntagma and converts it into the predicate of its clause.
The syntagma with which the copula forms the predicate (its syntactic operand) is a predicate complement. Despite its name, this is not a complement of the same kind as a complement of a verb because the copula does not govern it. Instead, the relation between the copula and the predicate complement is a syntactic relation sui generis.
Copulas may have different morphological properties cross-linguistically. Diachronically, they may be grammaticalized from items of different word classes, including importantly verbs and demonstrative pronouns. Likewise synchronically, they may be subclasses of diverse word classes.
A copula may be clitic. If it is, its phonological host does not necessarily coincide with its syntactic operand; i.o.w., the copula may cliticize to a word which is not a constituent of the predicate complement.
The inflection paradigm of the copula is often defective and/or suppletive in comparison with the word class of which it forms a subclass. Likewise, there are often forms only for marked verbal categories, while in present indicative clauses, there is no copula.
An affix of the same function as a copula is not a copula, but a verbalizer.
The same formative that functions as copula – typically, the verb ‘be’ – may function as the structural head in periphrastic constructions. There it is not a copula, but an auxiliary.