If there is a preposition following authority, it is often "of" indicating the source of authority. The prepositions "in" or "for" would indicate the scope of authority.
To have authority over something.
The noun, pronoun, or noun form that follows a preposition is its object. The object of the preposition is being connected to another word, by forming an adjective or adverbial prepositional phrase.
in
The preposition 'with' is used after compliance.
The preposition "in" typically follows the word "persists." For example, "The problem persists in spite of our efforts to solve it."
The preposition that typically follows the word pride is "in." For example, one might say "I take pride in my work."
The entire construction, including the preposition, is a prepositional phrase. What follows the preposition is a noun that is the "object of the preposition." This noun or noun form is what is being connected to the word the phrase modifies.
The preposition "from" typically follows the word "prohibited." For example: "Access to the restricted area is prohibited from all unauthorized personnel."
The noun or pronoun that follows the preposition is called the object of the preposition.
The noun, pronoun, or other noun form is called the object of the preposition. It is the word that the preposition relates to other words in the sentence, either as an adjective or an adverb phrase. There are commonly articles (a, an, the) or adjectives used with the object (e.g. in the large box).
The preposition "of" typically follows the word "aware." For example, "She is aware of the situation."
The object of the preposition is the noun that follows the preposition, the word that the preposition relates to another word in the sentence. It can also be a pronoun, gerund, infinitive, or noun phrase. Examples: The car is in the garage. (in is the preposition, and garage is the object of the preposition.) We went to the grocery store for milk. (the grocery store is the first object of a preposition; milk is the second object of a preposition.)