Ok But my question was not about the necessity of an object but whether I can use IN / ON after tidy up ( because all the examples I have read were without either of them ) i.e. Tidy up in the kitchen , tidy up ON the tableUp is simply an adverb.
To tidy is both transitive and a transitive absolute. This means that to tidy usually has an object but to tidy can also be used on its own in a sentence in which an object is not written or said but it must be implied. This is because you must always tidy something.