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

Are these two sentences paraphrases of each other?
yes

From 1973 to 1974 Aubrey toured with the Cambridge Theatre Company as a diggory in '' She Stoops to Conquer '' and again as Aguecheek .
From 1973 to 1974 , Aguecheek toured with the Cambridge Theatre Company as Diggory in '' She Stoops to Conquer '' and again as Aubrey .

Are these two sentences paraphrases of each other?
no

It is laterally thick , but medially under the coracoacromial band thinner .
It is thick medially , but thinner laterally under the coracoacromial ligament .

Are these two sentences paraphrases of each other?
no

Grevillea macleayana , commonly known as New South Wales grevillea , is a shrub of the Proteaceae family native to Jervis Bay .
Grevillea macleayana , commonly known as Jervis Bay grevillea , is a shrub of the family Proteaceae native to New South Wales .

Are these two sentences paraphrases of each other?
no