  The aim of this article is to study the Ext ring associated to a Koszul
$R$-ring and to use it to provide further characterisations of the former. As
such, for $R$ being a semisimple ring and $A$ a graded Koszul $R$-ring, we will
prove that there is an isomorphism of DG rings between
$\mathcal{E}(A):=\mathrm{Ext}^\bullet_A(R,R)$ and
$^{\ast-\text{gr}}\mathrm{T}(A) \simeq \mathrm{E}(^{\ast-\text{gr}\!} A)$.
Also, the Ext $R$-ring will prove to be isomorphic to the shriek ring of the
left graded dual of $A$, namely $\mathcal{E}(A) \simeq (^{\ast-\text{gr}\!}
A)^!$. As an application, these isomorphisms will be studied in the context of
incidence $R$-(co)rings for Koszul posets. Thus, we will obtain a description
and method of computing the shriek ring for $\Bbbk^c[\mathcal{P}]$, the
incidence $R$-coring of a Koszul poset. Another application is provided for
monoid rings associated to submonoids of $\mathbb{Z}^n$.
