A cohomological characteristic for the length and width of a partially ordered set |
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| Authors: | A. G. Sukhonos |
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| Affiliation: | 1.Institute of Applied Mathematics, Far East Division,Russian Academy of Sciences,Vladivostok,Russia |
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| Abstract: | 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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