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Mathematics of the USSR-Izvestiya, 1986, Volume 27, Issue 3, Pages 575–592
DOI: https://doi.org/10.1070/IM1986v027n03ABEH001194 (Mi im1402) 		 
This article is cited in 28 scientific papers (total in 28 papers)

Homotopy theory of coalgebras

V. A. Smirnov
English version PDF (963 kB) Citations (28) Russian version article
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DOI: https://doi.org/10.1070/IM1986v027n03ABEH001194
Abstract: This paper makes a study of operads and of coalgebras over operads. Certain operads $E_n$ and $E$ are defined, constituting the algebraic analogues of the "little $n$-cube" operads; it is then shown that the singular chain complex $C_*(X;R)$ of a topological space $X$ is a coalgebra over the operad $E$, and that this structure completely determines the weak homotopy type of the space.
Bibliography: 26 titles.
Received: 04.11.1983
Bibliographic databases:
UDC: 513.836
MSC: Primary 55P15, 55P47; Secondary 55U35, 18G30
Language: English
Original paper language: Russian
Citation: V. A. Smirnov, “Homotopy theory of coalgebras”, Math. USSR-Izv., 27:3 (1986), 575–592
Citation in format AMSBIB
\Bibitem{Smi85}
\by V.~A.~Smirnov
\paper Homotopy theory of coalgebras
\jour Math. USSR-Izv.
\yr 1986
\vol 27
\issue 3
\pages 575--592
\mathnet{http://mi.mathnet.ru/eng/im1402}
\crossref{https://doi.org/10.1070/IM1986v027n03ABEH001194}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=816858}
\zmath{https://zbmath.org/?q=an:0612.55012|0595.55008}
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    • This publication is cited in the following 28 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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