Meaning
Finite coherence type distinguishes coefficient systems that can be strictified from those with an intrinsic twist.
In the declared band-local equivalence theory, the package is called strictifiable when its associator class b_D is zero and intrinsically twisted when b_D is nonzero. The allowed equivalences matter: they must preserve the markings and validity data relevant to the construction.
Example (illustrative)
If Ω=δη for a permitted two-cochain η, modifying the tensor identifications by η⁻¹ removes that associator representative. If no permitted modification does this, the nonzero class records an intrinsic twist.
Scope and limits
Strictification is relative to the allowed equivalence theory. It does not mean erasing physical markings or replacing the full theory by one global Hilbert space.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 10.2.