HOMOTOPY THEORY OF COALGEBRAS

@inproceedings{Smirnov1986HOMOTOPYTO,
  title={HOMOTOPY THEORY OF COALGEBRAS},
  author={Valerii A. Smirnov},
  year={1986}
}
  • Valerii A. Smirnov
  • Published 1986
  • Mathematics
  • This paper makes a study of operads and of coalgebras over operads. Certain operads En 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. 

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 27 CITATIONS

    Iterating the Bar Construction

    VIEW 4 EXCERPTS
    CITES METHODS & BACKGROUND
    HIGHLY INFLUENCED

    Operadic Torsors

    VIEW 1 EXCERPT
    CITES BACKGROUND

    Steenrod coalgebras

    VIEW 1 EXCERPT
    CITES BACKGROUND

    Koszul duality of En-operads

    VIEW 1 EXCERPT
    CITES BACKGROUND

    Modules over monads and initial semantics

    VIEW 1 EXCERPT
    CITES BACKGROUND