Quadratic functors on pointed categories

Manfred Hartl (1) , Christine Vespa (2)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 IRMA - Institut de Recherche Mathématique Avancée

We study polynomial functors of degree 2, called quadratic, with values in the category of abelian groups Ab, and whose source category is an arbitrary category C with null object such that all objects are finite coproducts of a generating object E. A functorial equivalence is established between quadratic functors from C to Ab and certain minimal algebraic data. Applying this general result to the case where E is a cogroup these data take a particulary simple form. This application extends results of Baues and Pirashvili obtained for C being the category of free groups or modules of finite rank.

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]; Théorie des groupes [math.GR]

Manfred Hartl, Christine Vespa. Quadratic functors on pointed categories. 2008. ⟨hal-00334292v1⟩