If an object complement can be an adjective, noun, or pronoun, what is then "working at the desk" in this sentence?
I found Jack working at the desk
Why isn't it adverbial of place?
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I found Jack [working at the desk].
That [working at the desk] is an object complement, consisting of various grammatical elements. It's Jack who is [working at the desk].
working => Gerund-Participle form of verb, realised by a verb + ing. Here it indicates the action of Jack in progress at the time of my finding him.
at the desk => An adjunct, indicating the place where Jack's action is taking place at the time of my finding him. This adjunct is realised by a Prepositional Phrase (PP) - at the desk. The head preposition is - at and it's complement is a Noun Phrase (NP) - the (determiner) desk (head noun).