Groupes d'extensions et foncteurs polynomiaux

TL;DR

This paper characterizes small additive categories where the inclusion of analytic functors into all functors induces isomorphisms between extension groups, generalizing Pirashvili's work.

Contribution

It provides a new characterization of additive categories ensuring extension group isomorphisms for analytic functors, extending previous results by Pirashvili.

Findings

Identifies conditions on small additive categories for extension isomorphisms.

Generalizes Pirashvili's characterization to broader categories.

Establishes a link between analytic functors and extension groups.

Abstract

G\'en\'eralisant un article de Pirashvili, nous caract\'erisons les petites cat\'egories additives A telles que l'inclusion dans la cat\'egorie des foncteurs de A vers les groupes ab\'eliens de la sous-cat\'egorie pleine des foncteurs analytiques induise un isomorphisme entre groupes d'extensions. -- Extending an article of Pirashvili, we characterize small additive categories A such that the inclusion in the category of functors from A to abelian groups of the full subcategory of analytic functors induces an isomorphism between extension groups.