A cohomological bundle theory for sheaf cohomology

We develop a bundle theory of presheaves on small categories, based on similar work by Brent Everitt and Paul Turner. For a certain set of presheaves on posets, we produce a Leray–Serre type spectral sequence that gives a reduction property for the cohomology of the presheaf. This extends the usual cohomological reduction of posets with a unique maximum.

Keywords

sheaf cohomology, spectral sequence, bundle of presheaves

2010 Mathematics Subject Classification

05E45, 55N30, 55T05

Full Text (PDF format)

Received 15 March 2023

Received revised 9 June 2023

Accepted 12 June 2023

Published 29 May 2024