Une formule pour les extensions de foncteurs composés

Alain Troesch¹

¹ LAGA, Institut Galilée Université Paris 13 99, avenue J.-B. Clément 93430 Villetaneuse, France

Fundamenta Mathematicae, Tome 177 (2003) no. 1, pp. 55-82

Résumé

Let $p$ be a prime, and let ${\cal F}$ be the category of functors from the finite $\Bbb F_p$-vector spaces to all $\Bbb F_p$-vector spaces. The object $\rm Id$ of ${\cal F}$ is the inclusion functor. Let $F$ and $G$ be two objects in ${\cal F}$. If $F$ and $G$ satisfy suitable conditions, the main result of this paper allows one to compute $\mathop{{\rm Ext}}_{\cal F}^*(\mathop{{\rm Id}},G \circ F)$ from the knowledge of $\mathop{{\rm Ext}}_{\cal F}^*(\mathop{{\rm Id}},F)$ and $\mathop{{\rm Ext}}_{\cal F}^*(\mathop{{\rm Id}},G)$.

Détail

DOI : 10.4064/fm177-1-4

Mots-clés : prime cal category functors finite bbb p vector spaces bbb p vector spaces object cal inclusion functor objects cal satisfy suitable conditions main result paper allows compute mathop ext cal * mathop circ knowledge mathop ext cal * mathop mathop ext cal * mathop