On Triples, Operads, and Generalized Homogeneous Functors
| dc.creator | McCarthy, Randy | |
| dc.creator | Minasian, Vahagn | |
| dc.date | 2004-01-25 | |
| dc.date.accessioned | 2026-07-07T05:04:51Z | |
| dc.date.available | 2026-07-07T05:04:51Z | |
| dc.description | We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors $F: \A \to M_A$ from a pointed category with coproducts to $A$-modules in terms of differentials of $F$. Here $A$ is a commutative $S$-algebra. We specialize to the case when $\A$ is the category of $\a$-algebras for an operad $\a$ and $F$ is the forgetful functor, and derive milder splitting conditions in terms of the derivative of $F$. In addition, we describe how triples induce operads, and prove that, roughly speaking, a triple $T$ is naturally equivalent to the product of its Goodwillie layers if and only if it is an algebra over its induced operad. | |
| dc.identifier | https://arxiv.org/abs/math/0401346 | |
| dc.identifier | http://arxiv.org/abs/math/0401346 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69965 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P43; 18D50; 55P99 | |
| dc.title | On Triples, Operads, and Generalized Homogeneous Functors | |
| dc.type | text |