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Verbal categories and identities of universal algebras
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 2, pp. 125-141 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a characterization of varieties of universal algebras which are rationally equivalent to varieties of algebras over operads over arbitrary verbal categories.
Keywords: verbal category, operad, variety of algebras, free algebra, free operad.
Mots-clés : rational equivalence 
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S. N. Tronin. Verbal categories and identities of universal algebras. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 2, pp. 125-141. http://geodesic.mathdoc.fr/item/UZKU_2012_154_2_a12/

[1] Tronin S. N., “O kharakterizatsii mnogoobrazii algebr nad $W$-operadami”, Mezhdunar. algebr. konf., posvyasch. 250-letiyu Mosk. gos. un-ta i 75-letiyu kaf. vyssh. algebry, Tez. dokl., Izd-vo mekhmata MGU, M., 2004, 127–128

[2] Tronin S. N., “Operady i mnogoobraziya algebr, opredelyaemye polilineinymi tozhdestvami”, Sib. matem. zhurn., 47:3 (2006), 670–694 | MR | Zbl

[3] Tronin S. N., “Abstraktnye klony i operady”, Sib. mat. zhurn., 43:4 (2002), 924–936 | MR | Zbl

[4] Tronin S. N., “Multikategorii i mnogoobraziya mnogosortnykh algebr”, Sib. matem. zhurn., 49:5 (2008), 1185–1201 | MR | Zbl

[5] Tronin S. N., “Estestvennye multipreobrazovaniya multifunktorov”, Izv. vuzov. Matem., 2011, no. 11, 58–71 | MR | Zbl

[6] Bordman Dzh., Fogt R., Gomotopicheski invariantnye algebraicheskie struktury na topologicheskikh prostranstvakh, Mir, M., 1977, 408 pp. | MR

[7] Mei Dzh. P., “Geometriya iterirovannykh prostranstv petel”: Bordman Dzh., Fogt R., Gomotopicheski invariantnye algebraicheskie struktury na topologicheskikh prostranstvakh, Mir, M., 1977, 267–403 | MR

[8] Smirnov V. A., Operadnye i simplitsialnye metody v algebraicheskoi topologii, Faktorial Press, M., 2002, 272 pp.

[9] Leinster T., Higher Operads, Higher Categories, Cambridge Univ. Press, Cambridge, 2004, 448 pp. | MR | Zbl

[10] Markl M., Shnider S., Stasheff J., Operads in Algebra, Topology and Physics, Amer. Math. Soc., 2002, 350 pp. | MR | Zbl

[11] Markl M., “Operads and PROPs”, Handbook of Algebra, v. 5, Elsevier, North-Holland, Amsterdam, 2008, 87–140 | DOI | MR | Zbl

[12] Loday J.-L., Valette B., Algebraic Operads, Grundlehren der mathematischen Wissenschaften, 346, Springer-Verlag, 2012, XVIII+512 pp. URL: http://math.unice.fr/~brunov/Operads.pdf | DOI | MR | Zbl

[13] Tronin S. N., Gareeva L. D., “O nekotorykh operadakh, svyazannykh s operadoi simmetricheskikh grupp. I”, Izv. vuzov. Matem., 2004, no. 9, 61–72 | MR

[14] Dzhonston P., Teoriya toposov, Nauka, M., 1986, 440 pp. | MR

[15] Katsov E. B., “Tenzornoe proizvedenie funktorov”, Sib. matem. zhurn., 19:2 (1978), 318–327 | MR | Zbl

[16] MacLane S., Moerdijk I., Sheaves in Geometry and Logic: A First Introduction to Topos Theory, Springer, N.Y., 1992, 620 pp. | MR

[17] Maltsev A. I., “Strukturnaya kharakteristika nekotorykh klassov algebr”, Dokl. AN SSSR, 120:1 (1958), 29–32 | Zbl

[18] Pinus A. G., Uslovnye termy i ikh primenenie v algebre i teorii vychislenii, Izd-vo NGTU, Novosibirsk, 2002, 239 pp.