Monad interleaving: a construction of the operad for Leinster's weak $ω$-categories
| dc.creator | Cheng, Eugenia | |
| dc.date | 2003-09-20 | |
| dc.date | 2008-10-04 | |
| dc.date.accessioned | 2026-07-07T10:07:33Z | |
| dc.date.available | 2026-07-07T10:07:33Z | |
| dc.description | 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 functor $\owc \lra \coll$, from the category of operads-with-contraction to the category of collections. By applying this to the initial (empty) collection, we obtain explicitly an initial operad-with-contraction, whose algebras are by definition the weak $ω$-categories of Leinster. | |
| dc.description | 24 pages. Fuller explanations, updated bibliography. To appear in JPAA | |
| dc.identifier | https://arxiv.org/abs/math/0309336 | |
| dc.identifier | http://arxiv.org/abs/math/0309336 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170674 | |
| dc.subject | Category Theory | |
| dc.subject | 18D05; 18C15; 18D50 | |
| dc.title | Monad interleaving: a construction of the operad for Leinster's weak $ω$-categories | |
| dc.type | text |