Geodesic
Category of Chu spaces over $S-Act$ category
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1220-1237.

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We consider two categories of Chu spaces over the category of $ S-Act $. For the case when $ S $ is a commutative monoid, the questions of completeness, conjugate objects and the conditions of reflexivity of objects are studied in the categories under consideration.
Keywords: Chu spaces, $S-Act$, monoidal category, limit, functor.
Mots-clés : Chu construction, colimit 
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A. A. Stepanova; E. E. Skurikhin; A. G. Sukhonos. Category of Chu spaces over $S-Act$ category. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1220-1237. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a35/

[1] Barr M., *-Autonomous Categories, Lecture Notes in Math., 752, Springer-Verlag, Berlin, 1979 | DOI | MR | Zbl

[2] Barr M., “*-Autonomous categories, with an appendix by Po Hsiang Chu”, Lecture Notes in Mathematics, 1, 1991, 159–178 | MR | Zbl

[3] Barr M., Wells C., Category Theory for Computing Science, Prentice Hall international series computer science Spectrum Book, Prentice Hall, 1998 | MR

[4] Gould V., Mikhalev A. V., Palyutin E. A., Stepanova A. A., “Model-theoretic properties of free, projective, and flat S-acts”, Journal Math. Sci. New York, 164:2 (2010), 195–227 | DOI | MR | Zbl

[5] Kilp M., Knauer U., Mikhalev A. V., Monoids, Acts and Categories, Walter De Gruyter, Berlin, 2000 | MR | Zbl

[6] Kilp M., Knauer U., “On torsionless and Dense Acts”, Semigroup Forum, 63:3 (2001), 396–414 | DOI | MR | Zbl

[7] S. Mac Lane, Categories for the Working Mathematician, 2nd. edition, Springer, Berlin, 1997 | MR

[8] Pratt V. R., “Chu Spaces”, Notes for School on Category Theory and Applications, Textos Mat. Ser. B Coimbra: Univ. Coimbra, 21, 1999, 39–100 | MR | Zbl

[9] Skurikhin E. E., Sukhonos A. G., “Grothendieck Topologies on Chu Spaces”, Siberian Advances in Mathematics, 19:3 (2009), 192–210 | DOI | MR

[10] Stepanova A. A., “Axiomatizability and completeness of the class of injective acts over a commutative monoid or a group”, Siberian Mathematical Journal, 56:3 (2015), 516–525 | DOI | MR | Zbl