Why it is a question
Two clusters in the record treat meaning categorically and do not meet.
- Composition. DisCoCat (LIT-273, read in NOTE-245) composes word meanings along a pregroup parse into a sentence meaning. The Frobenius version (LIT-272, NOTE-246) gives relational words copy maps. Both are maps from a grammatical structure to vector spaces. Neither says anything about context of use or about carrying a meaning into another medium.
- Transport. The manuscript’s transport carries a context-indexed empirical model from one observational scenario to another (CLAIM-125). It treats an utterance’s observables as given, not as built from the observables of its parts.
The review that raised this put it as: “different constructions, but their categorical treatment of composition may help formalize the relationship between compositional linguistic structure and observational transport.”
There are two ways the comparison could turn out, and they differ.
- Composition constrains transport. A transport that respects the grammatical composition would be fixed on whole utterances by what it does on words and on the composition maps. A rendering that breaks the composition (a paraphrase that reparses) would then be visible as a failure of that respect.
- Composition stops at the proposition. What DisCoCat composes is propositional and distributional meaning. The manuscript argues that preserving the proposition is not sufficient to preserve the communicative act (CLAIM-061, with CLAIM-053’s correction). If footing and illocutionary force are not compositional in DisCoCat’s sense, the constraint covers only the part the manuscript says is not enough.
What would count as an answer
- A construction. Transport stated as a map between compositional models that commutes with the composition, together with a statement of which empirical-model properties it then preserves. The properties that matter are global compatibility and the noncontextual fraction (THEORY-174).
- A separation. A pragmatic observable the manuscript uses, such as footing or force, shown to be non-compositional over a parse: two utterances with the same parts and the same composition that differ on it. That would confine the comparison to propositional content.
Either settles the question. A further demonstration that DisCoCat and sheaves are both categorical does not.
What the record holds toward an answer
- The meeting point already exists. Abramsky and Sadrzadeh’s Semantic Unification (LIT-841, NOTE-644) builds a presheaf of discourse representations and glues sentence meanings over a cover of anaphoric resolutions. It is the record’s earliest bridge between the Abramsky–Brandenburger framework and semantics. Its obstruction to gluing is inconsistency of literals, not contextuality, and it has no transport.
- Contextuality in phrase meaning. Wang et al. (LIT-842, NOTE-645) test noun–verb phrases, which are compositional units, for contextuality. Their corpus estimates are almost always signalling. So the data on which a compositional constraint would be checked are the data CLAIM-125’s second open problem is about.
Note of 2026-10-11: material in the record that may bear on this
A synthesis review of 2026-10-11 found these entries bearing on this
question without being linked to it. Each is listed for what its title
says; none has yet been assessed as an answer, and none is linked by
answers.
- THEORY-017: In a Hilbert-space model only unitarily invariant structure is intrinsic; a basis or tensor factorisation,…