The partition poset complex and the Goodwillie derivatives of the identity in spaces
arXiv:2007.05440
Abstract
We produce a canonical highly homotopy-coherent operad structure on the derivatives of the identity functor in spaces via a pairing of cosimplicial objects, providing a new description of an operad structure on such objects first described by Ching. We prove that the two structures agree: both are restrictions of a single algebra over an operad of windowed cut systems on weighted trees, whose component spaces are contractible, along maps of structuring operads which are all levelwise weak equivalences. In addition, we show the derived primitives of a commutative coalgebra in spectra form an algebra over this operad.
arXiv comment47 pages, substantial expansion from v2
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