Definition 7.46.
The category of Stefanich rings is
\[\StRing
:=\colim_{1\Pr}\bigl(\CAlg(\An)\longrightarrow\CAlg(1\Pr)\longrightarrow\CAlg(2\Pr)\longrightarrow\cdots\bigr).\]
Equivalently,
\[\StRing
\simeq\lim_{\CAT}\bigl(\CAlg(\An)\longleftarrow\CAlg(1\Pr)\longleftarrow\CAlg(2\Pr)\longleftarrow\cdots\bigr),\]
where the transition functor sends a symmetric monoidal category to the endomorphism object of its unit. Thus a Stefanich ring may be written as a sequence \(A=(A_0,A_1,A_2,\ldots)\) with \(A_n\in\CAlg(n\Pr)\) and compatible isomorphisms
\[A_n\cong\End_{A_{n+1}}(\unit).\]