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A Diagonal on the Associahedra

Samson Saneblidze·Ronald Umble
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Abstract

Let C_*(K) denote the cellular chains on the Stasheff associahedra. We construct an explicit combinatorial diagonal Δ: C_*(K) --> C_*(K) \otimes C_*(K); consequently, we obtain an explicit diagonal on the A_\infty-operad. We apply the diagonal Δto define the tensor product of A_\infty-(co)algebras in maximal generality.

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Samson Saneblidze, Ronald Umble. 2004-06-07. A Diagonal on the Associahedra. https://arxiv.org/abs/math/0011065

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