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The structure of vocabulary

Language is a collection of concepts and the ways they interact. Concepts are bounded units. Interactions are the relations between them: definitional, derivational, cross-referential, idiomatic, narrowing, borrowing, and others. A language, in any bounded context, is both: concepts and the relations that operate on them. The concept is more general than in ordinary usage — subsets of vocabularies for specific use also count as languages here.

Vocabulary is the set of concepts within a bounded context. The bounded context can go from very small to large.

A category-theoretic view

The decomposition maps cleanly onto category theory:

• Concepts → objects.
• Vocabulary → the object set of a category, Ob(C), per bounded context.
• Relations → morphisms. Multiple kinds (definitional, derivational, idiomatic, cross-referential) coexist.
• A language within a bounded context → a category.
• Cross-context mappings (how one language game’s terms map into another’s) → functors between categories.

A functor carries both concepts and the relations among them. Translation in this frame isn’t term-for-term substitution but preservation of how things hang together.