Infinitive verb forms

“We ran quickly to catch the bus.”

In this sentence, is “to catch” an infinitive verb form? Also, is there such a thing as a definitive verb or subordinate verb form?

I would appreciate all help. Thank you.

Yes, based on this definition:

TO (preposition): used as the ordinary sign or accompaniment of the infinitive, as in expressing motion, direction, or purpose, in ordinary uses with a substantive object.

Of course we should consider that ‘to’ is a part also of an elided phrasal preposition, ‘in order to’, with ‘to catch the bus’ an infinitive clause of purpose.