Authors: Michael Robinson ¹

• 1 Mathematics and Statistics, American University, Washington, DC, USA

An assignment to a sheaf is the choice of a local section from each open set in the sheaf's base space, without regard to how these local sections are related to one another. This article explains that the consistency radius -- which quantifies the agreement between overlapping local sections in the assignment -- is a continuous map. When thresholded, the consistency radius produces the consistency filtration, which is a filtration of open covers. This article shows that the consistency filtration is a functor that transforms the structure of the sheaf and assignment into a nested set of covers in a structure-preserving way. Furthermore, this article shows that consistency filtration is robust to perturbations, establishing its validity for arbitrarily thresholded, noisy data.

• 18F20 - Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
• 55N05 - ?ech types
• 55N31 - Persistent homology and applications, topological data analysis
• 94A12 - Signal theory (characterization, reconstruction, filtering, etc.)

• 1 zbMATH Open