Monad interleaving: a construction of the operad for Leinster’s weak ω-categories
نویسنده
چکیده
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 operads-with-contraction 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 dimension-by-dimension free functors. Hence we give an explicit construction of a left adjoint for the forgetful functorOWC −→ Coll, from the category of operadswith-contraction to the category of collections. By applying this to the initial (empty) collection, we obtain explicitly an initial operad-withcontraction, whose algebras are by definition the weak ω-categories of Leinster.
منابع مشابه
A Homotopy-theoretic Universal Property of Leinster’s Operad for Weak Ω-categories
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