Far Eastern Mathematical Journal

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Cohomologies and dimensions of Chu spaces

E. E. Skurikhin, A. G. Sukhonos

2005, issue 1-2, P. 14–22

Abstract

We define Grothendieck topologies on Chu spaces and consider sheaf cohomologies, dimensions and cohomological dimensions of Chu spaces.

Keywords: Chu spaces, Grothendieck topologies, sheaf cohomology, dimension

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References

[1] M. Barr, ?-Autonomous categories, Lecture Notes in Mathematics, 752, Springer, Heidelberg, 1979. [2] V. R. Pratt, Chu spaces from the Representational Viewpoint, Preprint, 2005. [3] G.-Q. Zang, “Chu spaces, concept lattices, and domain”, Electronic Notes in Theoretical Computer Science, 83 (2004). [4] V. Gupta, V. R. Pratt, “Gates Accept Concurrent Behavior”, Proc. 34th Ann. IEEE Symp. on Foundations of Comp. Sci., 1993, 62–71. [5] V. R. Pratt, Chu spaces, Notes for school on category theory and applications, Technical report, University of Coimbra, Portual, 1999. [6] A. G. Suxonos, E'kvivalentnost' kategorij $chu_\sum#$ i $ps_\sum$, Preprint № 19 DVO RAN, Institut prikladnoj matematiki, Dal'nauka, Vladivostok, 2004, 20 s. [7] E. E. Skurixin, “Puchkovye kogomologii i razmernost' chastichno uporyadochennyx mnozhestv”, Tr. Mat. in-ta V. A. Steklova RAN, 239, 2002, 289–317. [8] E. E. Skurixin, Puchkovye kogomologii i razmernost' chastichno uporyadochennyx mnozhestv, Dal'nauka, Vladivostok, 2004, 194 s. [9] M. Artin, Grothendieck topologies, Lecture Notes, Harvard Math. Dept., 1962.

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