Geodesic
A cohomological characteristic for the length and width of a partially ordered set
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 217-227 
A. G. Sukhonos. A cohomological characteristic for the length and width of a partially ordered set. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 217-227. http://geodesic.mathdoc.fr/item/FPM_2009_15_7_a10/
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     title = {A~cohomological characteristic for the length and width of a~partially ordered set},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[2] Skurikhin E. E., “Puchkovye kogomologii i razmernost chastichno uporyadochennykh mnozhestv”, Tr. MMO, 239, 2002, 289–317 | MR | Zbl

[3] Skurikhin E. E., Puchkovye kogomologii i razmernost chastichno uporyadochennykh mnozhestv., Dalnauka, Vladivostok, 2004

[4] Skurikhin E. E., Kogomologii i razmernosti topologicheskikh i ravnomernykh prostranstv, Dalnauka, Vladivostok, 2008

[5] Skurikhin E. E., Sukhonos A. G., “Topologiya Grotendika na prostranstvakh Chu”, Mat. tr., 11:2 (2008), 159–186 | MR | Zbl

[6] Artin M., Grothendieck Topologies, Amer. Math. Soc., 1962