On Local Coefficients of Simplicial Coalgebras
نویسندگان
چکیده
This paper generalizes the notion of local coefficients and fundamental groups of spaces to simplicial coalgebras. We define a Hopf algebra π1(C) from a simplicial coalgebra C as a generalization of a fundamental group, and show that a module overπ1(C) corresponds to a local coefficient of C. As a consequence, the Hoschild cohomology of a Hopf algebraH with a coefficient M coincides with the cohomology of the nerve simplicial coalgebra of H with the local coefficientM∗ associated withM .
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