Geodesic
On algebras over multicategories
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2016), pp. 62-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce a notion of a monoidal category over verbal category. In such categories we define algebras over multicategories over the same verbal categories. We also explicitly compute categories of algebras for two classes of multicategories.
Keywords: verbal category, multicategory, multifunctor, algebra over multicategory, commutative operad.
Mots-clés : natural multitransformation 
@article{IVM_2016_2_a8,
     author = {S. N. Tronin},
     title = {On algebras over multicategories},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {62--74},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_2_a8/}
}
TY  - JOUR
AU  - S. N. Tronin
TI  - On algebras over multicategories
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2016
SP  - 62
EP  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2016_2_a8/
LA  - ru
ID  - IVM_2016_2_a8
ER  - 
%0 Journal Article
%A S. N. Tronin
%T On algebras over multicategories
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2016
%P 62-74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2016_2_a8/
%G ru
%F IVM_2016_2_a8
S. N. Tronin. On algebras over multicategories. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2016), pp. 62-74. http://geodesic.mathdoc.fr/item/IVM_2016_2_a8/

[1] Tronin S. N., “Estestvennye multipreobrazovaniya multifunktorov”, Izv. vuzov. Matem., 2011, no. 10, 58–71 | MR | Zbl

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

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

[4] Tronin S. N., “Multikategorii i mnogoobraziya mnogosortnykh algebr”, Sib. matem. zhurn., 49:5 (2008), 1184–1201 | MR

[5] Tronin S. N., Kopp O. A., “Matrichnye lineinye operady”, Izv. vuzov. Matem., 2000, no. 8, 53–62 | MR | Zbl

[6] Kelly G. M., Street R., “Review of the elements of 2-categories”, Category Seminar, Proceedings of Sydney Category Seminar 1972/1973, Lect. Notes Math., 420, Springer Verlag, Berlin–Heidelberg, 1974, 75–103 | DOI | MR

[7] Maklein S., Kategorii dlya rabotayuschego matematika, Fizmatlit, M., 2004

[8] Borceux F., Handbook of categorical algebra, v. 2, Categories and structures, Cambridge University Press, 1994 | MR | Zbl

[9] Leinster T., Higher operads, higher categories, London Math. Soc. Lect. Notes Ser., 298, Cambr. Univ. Press, 2003 | MR

[10] Artamonov V. A., “Klony polilineinykh operatsii”, UMN, 24:1 (1969), 47–59 | MR | Zbl

[11] Tronin S. N., “Algebry nad operadoi sfer”, Izv. vuzov. Matem., 2010, no. 3, 72–81 | MR | Zbl

[12] Dzhonston P., Teoriya toposov, Nauka, M., 1986 | MR

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

[14] Hermida C., “Representable multicategories”, Adv. Math., 151:2 (2000), 164–225 | DOI | MR | Zbl