The preposition is in the shed is the object of the preposition. The prepositional phrase is in the shed. The phrase modifies left (a verb). (It tells us where). The phrase is an adverbial phrase
To find the object of the preposition, you must ask yourself what is the preposition referring to? In this case, "the gardener left her tools in the shed", the preposition is "in". You should ask "in what"? And you'll find The Shed. So, in this case, the shed is the noun
