For a finite dimensional algebra Λ of finite representation type and an additive generator M for modΛ, we investigate the properties of the Yoneda algebra Γ=⨁i≥0ExtΛi(M,M)
Nearby in the stack
. We show that
Γ
is graded coherent and Gorenstein of self-injective dimension at most
1
, and the graded singularity category
DsgZ(Γ)
of
Γ
is triangle equivalent to the derived category of the stable Auslander algebra of
Λ
. These results remain valid for representation-infinite algebras. For this we introduce the Yoneda category
Y
of
Λ
as the additive closure of the shifts of the
Λ
-modules in the derived category
Db(modΛ)
. We show that
Y
is coherent and Gorenstein of self-injective dimension at most
1
, and the singularity category of
Y
is triangle equivalent to the derived category
Db(mod(modΛ))
of the stable category
modΛ
. To give a triangle equivalence, we apply the theory of realization functors. We show that any algebraic triangulated category has an f-category over itself by formulating the filtered derived category of a DG category, which assures the existence of a realization functor.