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 .
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 .

Are these two sentences paraphrases of each other?
yes

In 1986 he joined forces with Edgeworth David to work together on the ANARE expedition that established the Sir Erich A. Colhoun summer field base in the Bunger Hills .
In 1986 , he joined Edgeworth David to work together on the ANARE expedition that founded the summer field base of Sir Erich A. Colhoun in the Bunger Hills .

Are these two sentences paraphrases of each other?
yes

The Eastern Australian Football League is an Australian rule football competition in the eastern United States of America and a department of the United States Australian Football League .
The United States Australian Football League is an Australian rule football competition in the eastern United States of America and a division of the Eastern Australian Football League .

Are these two sentences paraphrases of each other?
no

He was also trained at the Academy of Art in Zurich , where he and others learned musically to use the computer for composing music .
He was musically trained at the academy of art in Zurich , where he and others also learned how to use the computer for composing music .

Are these two sentences paraphrases of each other?
no