This work demonstrates an E2-action on a homotopy limit through a new operad mapping, indicating significant implications for algebraic topology.
We construct a map of operads from an E₂-operad to the condensation of the operad for multiplicative hyperoperads. We deduce from it the existence of an E₂-action on the homotopy limit of the underlying functor of a multiplicative hyperoperad. This result is the higher dimensional analogue of a result due to Batanin and Berger implying Deligne's conjecture.
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Leger et al. (2025) studied this question.
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