剪子同调的同调束理论

Pub Date : 2024-05-29 DOI:10.4310/hha.2024.v26.n1.a20

Mihail Hurmuzov

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引用次数: 0

摘要

我们以布伦特-埃弗里特和保罗-特纳的类似研究为基础，发展了小范畴上预设的束理论。对于正集上的某组预设，我们产生了一个勒雷-塞尔型谱序列，给出了预设的同调还原特性。这扩展了具有唯一最大值的正集的通常同调还原。

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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.

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