%
\label{def:e1-layer}
$\Estage{1}$ denotes Category~$\T$
equipped with the self-enrichment data
earned in Part~VIII.
Explicitly, $\Estage{1}$ adds to~$\Estage{0}$
the following structures:
\begin{enumerate}
    \item \textbf{Hom objects as $\T$-objects.}
          For all $A, B \in \Obj(\T)$,
          the morphism space $\Hom(A,B) \in \Obj(\T)$
          (II.D53, II.D54,
          Chapter~\ref{ch:tau-self-enrichment}).
          Each Hom object has an NF address,
          inherits bipolar decomposition,
          and satisfies tower coherence.

    \item \textbf{The Yoneda embedding.}
          $\T \hookrightarrow [\T^{\op}, \T]$
          is a full and faithful functor
          (II.T36,
          Chapter~\ref{ch:yoneda-theorem}).
          This makes every $\T$-object
          representable by the morphisms into it.

    \item \textbf{2-categorical structure.}
          2-morphisms
          $\Hom(\Hom(A,B), \Hom(C,D))$
          are $\T$-objects
          (II.D55, II.D56,
          Chapter~\ref{ch:two-categories}).
          Morphisms between morphisms
          are first-class citizens.

    \item \textbf{Internal function spaces.}
          The internal Hom
          $[A,B] \in \Obj(\T)$
          replaces the external function set
          $\{f \colon A \to B\}$.
          Function spaces are objects,
          not meta-level collections.

    \item \textbf{The Code/Decode bijection.}
          $\mathrm{Code} \colon \mathcal{O}(\tau^3)
          \to \mathrm{Streams}(R_\tau, H_\tau)$
          and its inverse $\mathrm{Decode}$
          (II.T35,
          Chapter~\ref{ch:code-decode})
          internalize the Mutual Determination
          as a coding-theoretic bijection.

    \item \textbf{Self-referential capability.}
          $\T$ can talk about its own morphisms,
          compare them,
          and transform them---all
          within its own language
          (Remark~\ref{rem:self-description}, II.R15).
\end{enumerate}

\noindent
The transition $\Estage{0} \to \Estage{1}$
is what Part~VIII accomplishes.
$\Estage{1}$ is not a different category;
it is the \emph{same} category~$\T$,
now recognized as carrying self-enrichment structure
that was latent in $\Estage{0}$
but not yet articulated.