Is there a name for this when we omit "avere" in front of participle (trovato)?
Can we do the same with "essere" ?
(Andato sulla spiaggia, ho riposato un può - Having gone to the beach, I relaxed a bit) ?
Participles have many uses and can function also as nouns and adjectives. When it shows up without the auxiliary, it has a passive function, but it is still a verb. The same thing can be done with essere!