We construct a family of dualities on some subcategories of the quasi-category
S
\mathcal {S}
of self-small groups of finite torsion-free rank which cover the class
S
\mathcal {S}
. These dualities extend several of those in the literature. As an application, we show that a group
A
∈
S
A\in \mathcal {S}
is determined up to quasi–isomorphism by the
Q
\mathbb {Q}
–algebras
{
Q
Hom
(
C
,
A
)
:
C
∈
S
}
\{\mathbb {Q}\operatorname {Hom}(C,A):\,C\in \mathcal {S}\}
and
{
Q
Hom
(
A
,
C
)
:
C
∈
S
}
\{\mathbb {Q}\operatorname {Hom}(A,C):\,C\in \mathcal {S}\}
. We also generalize Butler’s Theorem to self-small mixed groups of finite torsion-free rank.