Meaning
The admissible Grassmannian transport category organizes allowed projection-selected subspaces and the certified passages between them.
A Grassmannian parameterizes subspaces; here the subspaces are represented by admissible projections in the relevant Hilbert-module carrier. A passage is an adjointable comparison map, a partial isometry on its selected support, satisfying the module, physical-form, reference, and twisted-localization conditions. Composition uses the specified carrier comparison cells.
Example (illustrative)
On C³, projections P=diag(1,0,0) and Q=diag(0,1,0) select two lines. The map e₁↦e₂ is a partial isometry between them. It models the support condition; the physical and coherence conditions would still have to be supplied.
Scope and limits
An arbitrary path between subspaces is not automatically an admissible physical transport. The module and comparison data are part of the definition.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 3.1.