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Monad interleaving: a construction of the operad for Leinster’s weak ωcategories, Preprint, 2003, available at http://arxiv.org/abs/math/0309336
"... We show how to “interleave ” the monad for operads and the monad for contractions on the category Coll of collections, to construct the monad for the operadswithcontraction of Leinster. We first decompose the adjunction for operads and the adjunction for contractions into a chain of adjunctions ea ..."
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We show how to “interleave ” the monad for operads and the monad for contractions on the category Coll of collections, to construct the monad for the operadswithcontraction of Leinster. We first decompose the adjunction for operads and the adjunction for contractions into a chain of adjunctions each of which acts on only one dimension of the underlying globular sets at a time. We then exhibit mutual stability conditions that enable us to alternate the dimensionbydimension free functors. Hence we give an explicit construction of a left adjoint