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

yes

1. There are different types of average polymer molecular weight , which can be measured in different experiments .
2. There are different types of molecular polymer - average weight that can be measured in different experiments .

no

1. Collins introduced himself to the modern Barnabas Collins family as a cousin from England , a hard-working businessman never seen during the day .
2. Collins introduced himself to the modern Barnabas Collins family as a cousin from England , a hard-working businessman who was never seen during the day .
yes