Far Eastern Mathematical Journal

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A generalized Dilworth and Gleason theorem

Skurikhin E.E.

2021, issue 2, P. 257–267 DOI: https://doi.org/10.47910/FEMJ202122

Abstract

The theorem of R.P. Dilworth and A.M. Gleason is a generalization of a Cantor theorem. We propose and proof the generalized Dilworth and Gleason theorem for functors with codomain $K/D$.

Keywords: presheaves of sets, actions of semigroups on sets, preorders

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References

[1] R.P. Dilworth, A.M. Gleason, “A generalized Cantor theorem”, Proc. Amer. Math. Soc, 13 (1962), 704–705. [2] P. Kon, Universal'naia algebra, Mir, M., 1968. [3] A. Grothendieck (with M. Artin and J.-L. Verdier), Seminaire Geometrie Algebrique 4 [SGA4], Theorie de topos et cohomologie etale de schemas, Lect. Notes in Math. V. 269, 270, Springer, Heidelberg, 1972. [4] S. Maklein, Kategorii dlia rabotaiushchego matematika, Fizmatlit, M., 2004.

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