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If K and L are chain complexes of abelian groups (to which we restrict ourselves throughout this paper), then 
denotes the graded hyperhomology group of K and L, as defined in Car tan and Eilenberg (1) by means of free double complex resolutions of K and L. Hyperhomology groups have proved convenient in proving various versions of the Künneth theorem (see, for example, (4; 1; 2)).
