Omit same verbs in list of clauses

Question

First, I have to admit that I don't know a good term to refer to this case, nor do I have a concrete example. Everything is just from a vague memory. So if you can correct me or suggest a good correction, please feel free to do so.

I believe that I have sometimes come across a sentences in which the authors have some sorts of list of descriptions but only form a full clause for the first item of the list, and leave the second and third with just [subject object]. I don't know if it is a correct (and good) thing to do, but it amuses me somehow and I'd like to understand it better.

The sentence is something like this (this is my example, I don't have a good recall what I have come across):

Bushes should be categorized as trimmable, while trees (should be categorized) as obstacles, and grass (should be categorized) as terrains.

My sentence could be a lousy one or in the context that can be written in this way, but hope that you get my point

EDITED: keeping "as" as suggested

Answer 1

This is a specific type of ellipsis, gapping. According to Wikipedia:

In linguistics, gapping is a type of ellipsis that occurs in the non-initial conjuncts of coordinate structures. Gapping usually elides minimally a finite verb and further any non-finite verbs that are present.

As it says, it's the verb that gets elided, not prepositions (meaning you should keep "as", like @marcellothearcane said). Wikipedia has a similar example (subscript is the elided part):

Jim has been being observed by me, and Tom _{has been being observed} by you

Answer 2

From the tags it seems you already know the term—ellipsis. Here's a live example for you from The Devil's Dictionary:

EDIBLE, adj. Good to eat, and wholesome to digest, as a worm to a toad, a toad to a snake, a snake to a pig, a pig to a man, and a man to a worm.

@marcellothearcane is correct in suggesting to keep the as before every entry.

You shall find more examples in classic English literature of the eighteenth and nineteenth centuries.

EDIT: Here is another example I have just read in As a Man Thinketh:

The dishonest man may have some admirable virtues which the other does not possess; and the honest man obnoxious vices which are absent in the other.

EDIT2: Here is a classic quote for you, from Francis Bacon:

Reading maketh a full man; conference a ready man; and writing an exact man.