I saw him sitting on the bench.

Is sitting being used as an adjective?
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Comments  (Page 2) 
Hi Goodman

I believe we disagee only occasionally.

Best wishes
Look at the two sentences -
Case -1
1) He is sitting on the bench
2) I saw him sitting on the bench

Next two sentences
Case - 2
1) He is entering a room
2) I saw him entering a room

In the case 1, the action sitting is not indicating that he is in the process of sitting but indicates that he has already sat and he continues to be in that state.

In the case 2, the action entering is indicating that he is doing the action of entering

The verb sit is used in both the ways - sit down - meaning doing the action of sitting. So changing his position from standing to sitting is sitting down.
Someone who is already sitting wants to get up and go. His friend says sit for a while and then go. He doesn't intend to say that change the position. He just means that be the state in which you are.

Hence, sitting has two meanings in it. Therefore, 'sitting' should be judged from the standpoint of its meaning and not just the word.
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I saw him sitting on the bench.

This is a complex catenative construction. "Saw" is a catenative verb with the subordinate participial clause "sitting on the bench" a catenative complement, and "him" the intervening noun. The subordinate clause is interpreted with progressive aspectuality: "He was sitting on the bench".