Sentence 1: A systematic study of category theory then allows us to prove mathematical results about any of these types of general structures from the axioms of a category .
Sentence 2: A systematic study of category theory then allows us to prove general results about each of these types of mathematical structures from the axioms of a category .

Do these two sentences convey the same information?

Pick your answer from:
[a]. no;
[b]. yes;
[a].