Every small monoidal category with universal finite joins of central idempotents is monoidally equivalent to the global sections a sheaf local categories on topological space. stiff embeds into such sections. An infinitary version these theorems also holds in spatial case. These representation results are functorial and subsume Lambek–Moerdijk–Awodey for toposes, Stone Boolean algebras, Takahas...

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse-theoretic techniques. As a consequence, we derive efficient techniques for distributed computation of (ordinary) cohomology of a cell complex.

Every three-dimensional complex algebraic variety with isolated singular point has a resolution factoring through the Nash blowup and the blowup of the maximal ideal over which the second Fitting ideal sheaf is locally principal. In such resolutions one can construct Hsiang-Pati coordinates and thus obtain generators for the Nash sheaf that are the differentials of monomial functions.

The present paper, which is intended for a diverse audience of evaluation researchers, applied social scientists and research funders, provides a broad overview of the conceptual and statistical issues involved in using multi-site randomized trials to learn about and from variation in program effects across individuals, across policy-relevant and theoretically-relevant subgroups of individuals ...

An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a “maximally destabilizing” 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.