Object and Complement
In other cases the predicate consists of the Predicator followed by one or more central constituents that complete the meaning. The two main functional categories which occur in post-verbal position are the Object (O) as in 3 and the Complement (C) as in 4:

Without these, each of the above clauses would be incomplete both semantically and syntactically: [*The students carried] and [*Jo is], respectively. There are two main types of Object, the Direct Object (Od) as in 5, and the Indirect Object (Oi) as in 6. If there is only one Object, it will be the Direct Object.

Semantically, the objects encode the key participants in the event other than the subject: dark suits, an email (Od) and me (Oi) in these examples. Note that participants include not only human referents, but inanimate things and abstractions.
Complements encode constituents that, semantically, are not participants but are nevertheless normally required both syntactically and semantically, such as useful in 7 and President in 8.
There are two main types of Complement, the Complement of the Subject (Cs) (Subject Complement) as in 7a and 8a, and the Complement of the Object (Object Complement) (Co), as in 7b and 8b:

The Subject Complement and Object Complement do not encode a different kind of participant. Rather, they characterize or identify the Subject or the Object, respectively.
The basic clause structures formed by configurations of these functions are as follows:
S-P S-P-Od S-P-Oi-O d S-P-C S-P-Od-Co