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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 273, Pages 54–71
(Mi tm3287)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
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, Trudy Mat. Inst. Steklova, 273, MAIK Nauka/Interperiodica, Moscow, 2011, 54–71; Proc. Steklov Inst. Math., 273 (2011), 48–63
Linking options:
https://www.mathnet.ru/eng/tm3287 https://www.mathnet.ru/eng/tm/v273/p54
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Abstract page: | 530 | Full-text PDF : | 142 | References: | 114 |
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