2004/01/25 by Randy McCarthy, McCarthy, Randy, Vahagn Minasian +1
Mathematics · #18D50 #55P43 #55P99 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:18D50 #msc:55P43 #msc:55P99
paper · pdf · doi:10.48550/arxiv.math/0401346
arxiv created 2004/01/25 · openalex publication_date 2004/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors F: \A → MA 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.