Hi! The underlined are both nouns aren't they? Thanks, Fulvio
1. Are you interested in going hunting?
2. Are you interested in going shopping?
They are gerunds, which are like verbal nouns.
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Are you interested in going hunting / shopping?
The salient interpretation is that "hunting" and "shopping" are gerund-participle verbs functioning as heads of non-finite clauses.
"Go" is a catenative verb and the clauses "hunting" and "shopping" are its catenative complements.
Noun interpretation can be forced by adjectival premodification, a