Abstract
We describe a homotopy-theoretic approach to the theory of moduli of realizations of Blanc-Dwyer-Goerss, reproducing their obstructions to realizing a given Π-algebra as homotopy groups of a pointed space. Our techniques are based on the ∞-category PΣ(Sph) of product-preserving presheaves on finite wedges of positive-dimensional spheres, leading to more conceptual and streamlined arguments.
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