Why is the present progressive "going" used here? Is it ok if I just say "go up"?
To "go up" in this context is a phrasal verb of "go" and refers to something being built or put up somewhere. The progressive form "going" is used here because the action of a sign being put up in the library is told as a hypothetical situation, and so the verb can be progressive to indicate continuation. "Going" can replaced with "being" here or "being put up", and "being" also indicates continuation.
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