Abstract
We introduce a finitely presented prop S = { S ( n , m ) } in the category of differential graded modules whose associated operad U ( S ) = { S ( 1 , m ) } is a model for the E ∞ -operad. This finite presentation allows us to describe a natural E ∞ -coalgebra structure on the chains of simplicial sets in terms of only three maps: the Alexander-Whitney diagonal, the augmentation map, and an algebraic version of the join of simplices. The first appendix connects our construction to the Surjection operad of McClure-Smith and Berger-Fresse. The second establishes a duality between the diagonal and join maps for chains of augmented and non-augmented simplicial sets. A follow up paper constructs a prop corresponding to S in the category of CW-complexes.
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