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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^…
A cubical model for a fibration
Tornike Kadeishvili, Samson Saneblidze
In the paper the notion of truncating twisting function from a simplicial set to a cubical set and the corresponding notion of twisted Cartesian product of these…
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…
Galois theory and a new homotopy double groupoid of a map of spaces
R. Brown, G. Janelidze
The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new homo…