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Operads and algebraic homotopy

Justin R. Smith
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Abstract

This paper proves that the homotopy type of a pointed, simply-connected, 2-reduced simplicial set is determined by the chain-complex augmented by functorial diagonal and higher diagonal maps (a simple generalization of the ones used to define Steenrod operations). The treatment of this problem is completely self-contained, and includes material that simplifies, extends, and corrects material from the authors AMS Memoir, "Iterating the cobar construction".

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Justin R. Smith. 2000-08-09. Operads and algebraic homotopy. https://arxiv.org/abs/math/0004003

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