FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 7, PAGES 217-227

A cohomological characteristic for the length and width of a partially ordered set

A. G. Sukhonos

Abstract

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Grothendieck topologies on a poset preset by one set and corresponding sheaf cohomologies are analyzed. The relation between the given cohomologies and the length of a poset is identified. For this purpose, Grothendieck topologies are defined on the set of the chains and antichains of the given poset; the corresponding theories of sheaf cohomologies are formed and with the help of those the poset is analyzed.

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Last modified: April 18, 2010