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CoHochschild homology of chain coalgebras. (English) Zbl 1238.16005

The authors introduce a co-Hochschild homology theory for chain coalgebras over a principal ideal domain, generalizing a construction by Y. Doi [J. Math. Soc. Japan 33, 31-50 (1981; Zbl 0459.16007)]. The co-Hochschild complex is natural with respect to chain coalgebra morphisms up to homotopy. In particular this applies to the normalized chain complex of a reduced simplicial set, whose co-Hochschild complex turns out to be a homotopy-coassociative chain coalgebra. It should be noted that statements from this paper are needed in other recent papers of the first named author.

MSC:

16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
16T15 Coalgebras and comodules; corings
55U10 Simplicial sets and complexes in algebraic topology
55N99 Homology and cohomology theories in algebraic topology

Citations:

Zbl 0459.16007
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Full Text: DOI arXiv

References:

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