Meaning
A strict defect coefficient system provides consistently composable additive coordinates for measuring comparison failures.
It consists of two presheaves of defect coefficients and a natural map Q between them. Their restriction maps compose exactly. This makes the associated Čech differentials and mapping-fiber differential well defined. The physical comparisons being measured can still compose only up to specified cells.
Example (illustrative)
For three nested admitted regions, restricting a scalar defect from the largest to the smallest must give the same result directly or through the middle region. That is strictness of the bookkeeping, even if the physical maps carry a nontrivial comparison cell.
Scope and limits
Strict coefficients do not imply strict physical transport. If the coefficients themselves are only weakly composable or nonadditive, the ordinary cochain-complex notation requires a replacement construction.
Source
GAT 0 — Finite Cohomological and Coercive Recognition. GAT 0, Definition 9.1.