sentence1: transfer of properties under liaison the goal of this section is to illustrate how the existence of the maps φ and ψ can be used to show that cohomological and structural properties are preserved within m-liaison classes .
sentence2: resolutions of e-type and q-type the purpose of this section is to show the existence of maps φ and ψ from the set of even liaison classes into the set of stable equivalence classes of certain reflexive modules .