API development for `LanguageOn` in symbolic dynamics

This issue collects planned basic properties of the language of a subshift. The goal is to gradually build a small, reusable API for symbolic dynamics in the ambient full shift setting, consistent with the current design philosophy of avoiding subshift-relative definitions.

1. Basic monotonicity and functoriality

For subsets of configurations:

• Monotonicity

$X \subseteq Y \Rightarrow \mathcal{L}_U(X) \subseteq \mathcal{L}_U(Y)$

This will be the object of the first PR.

• Union compatibility

$\mathcal{L}_U(X \cup Y) = \mathcal{L}_U(X) \cup \mathcal{L}_U(Y)$

• Intersection inclusion

$\mathcal{L}_U(X \cap Y) \subseteq \mathcal{L}_U(X) \cap \mathcal{L}_U(Y)$

(equality is not expected in general)

2. Interaction with restriction in the shape

For finite shapes U ⊆ V, we have compatibility with restriction of patterns:

• Natural restriction map:

$\mathcal{L}_V(X) \to \mathcal{L}_U(X)$

induced by restricting patterns from V to U.

This should make the family (𝓛_U(X))_U functorial in the finite set U.

3. Interaction with subshifts

For a subshift Y : Subshift A G:

• 𝓛_U(Y) is defined via the carrier Y.carrier, hence inherits ambient properties.

Potential lemmas include:

• compatibility of language with shift invariance (at the level of induced patterns),
• stability under inclusion of subshifts:

$Y_1 \subseteq Y_2 \Rightarrow \mathcal{L}_U(Y_1) \subseteq \mathcal{L}_U(Y_2)$

This is expected to become relevant for later development of subshift classification and entropy.

Start by locating the existing LanguageOn definition and the Subshift A G carrier used in the issue. Implement and verify the first planned property, monotonicity for subsets, before addressing the later union, restriction, or subshift lemmas.