Contravariantly finite subcategories closed under predecessors

Let A be an Artin algebra and mod A be the category of finitely generated right A-modules. We prove that an additive full subcategory C of mod A closed under predecessors is contravariantly finite if and only if its right Ext-orthogonal is covariantly finite, or if and only if the Ext-injectives in C define a cotilting module (over the support algebra of C) or, equivalently, if and only if C is the support of the representable functors given by the Ext-injectives. (C) 2009 Elsevier Inc. All rights reserved.

NSERC of Canada

NSERC of Canada

Universite de Sherbrooke

Universite de Sherbrooke

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

FAPESP