78 citations · 83 across the 3 of their papers we have counts for
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The bar construction of an algebra as an E-infinite Hopf algebra
Benoit Fresse
We prove that the bar construction of an algebra forms an algebra. To be more precise, we provide the bar construction of an algebra over the surjection opera…
Koszul duality of operads and homology of partition posets
Benoit Fresse
We consider partitions of a set with elements ordered by refinement. We consider the simplicial complex formed by chains of partitions which starts at the smallest…
Derived division functors and mapping spaces
Benoit Fresse
The normalized cochain complex of a simplicial set N^*(Y) is endowed with the structure of an E_{infinity} algebra. More specifically, we prove in a previous article that N^*(Y) is…
A prismatic decomposition of the Barratt-Eccles operad
Clemens Berger, Benoit Fresse
The Barratt-Eccles operad is a simplicial operad formed by the classical homogeneous bar construction of the symmetric groups. We prove that these simplicial sets decompose as unio…
Combinatorial operad actions on cochains
Clemens Berger, Benoit Fresse
A classical E-infinity operad is formed by the bar construction of the symmetric groups. Such an operad has been introduced by M. Barratt and P. Eccles in the context of simplicial…