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Tr. Mat. Inst. Steklova, 2011, Volume 273, Pages 54–71 (Mi tm3287)  

Classifying vectoids and operad kinds

Nikolai V. Durov

St. Petersburg Department of the Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: A new generalisation of the notion of space, called vectoid, is suggested. Basic definitions, examples and properties are presented, as well as a construction of direct product of vectoids. Proofs of more complicated properties not used later are just sketched. Classifying vectoids of simplest algebraic structures, such as objects, algebras and coalgebras, are studied in some detail afterwards. Such classifying vectoids give interesting examples of vectoids not coming from spaces known before (such as ringed topoi). Moreover, monoids in the endomorphism categories of these classifying vectoids turn out to provide a systematic approach to constructing different versions of the notion of an operad, as well as its generalisations, unknown before.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2011, 273, 48–63

Bibliographic databases:

UDC: 512.581.7
Received in December 2009

Citation: Nikolai V. Durov, “Classifying vectoids and operad kinds”, Modern problems of mathematics, Collected papers. In honor of the 75th anniversary of the Institute, Tr. Mat. Inst. Steklova, 273, MAIK Nauka/Interperiodica, Moscow, 2011, 54–71; Proc. Steklov Inst. Math., 273 (2011), 48–63

Citation in format AMSBIB
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\by Nikolai~V.~Durov
\paper Classifying vectoids and operad kinds
\inbook Modern problems of mathematics
\bookinfo Collected papers. In honor of the 75th anniversary of the Institute
\serial Tr. Mat. Inst. Steklova
\yr 2011
\vol 273
\pages 54--71
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3287}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2893543}
\zmath{https://zbmath.org/?q=an:1235.18006}
\elib{http://elibrary.ru/item.asp?id=16456343}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 273
\pages 48--63
\crossref{https://doi.org/10.1134/S0081543811040055}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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