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math.AT2004
The Biderivative and A_\infty-bialgebras
Samson Saneblidze, Ronald Umble
An A_\infty-bialgebra is a DGM H equipped with structurally compatible operations {ω^{j,i} : H^{\otimes i} --> H^{\otimes j}} such that (H,ω^{1,i}) is an A_\infty-algebra and (H,ω^…
math.AT2002
Diagonals on the Permutahedra, Multiplihedra and Associahedra
Samson Saneblidze, Ronald Umble
We construct an explicit diagonal Δ_P on the permutahedra P. Related diagonals on the multiplihedra J and the associahedra K are induced by Tonks' projection P --> K and its factor…