Projective Dimensions in Cluster-Tilted Categories

Details Projective Dimensions in Cluster-Tilted Categories Projective Dimensions in Cluster-Tilted Categories

2011-11-13

arxiv.org/abs/1111.3077v1

Mathematics

Representation Theory

10 pages

Scientific paper

We study the projective dimensions of the restriction of functors Hom(-,X) to a contravariantly finite rigid subcategory T of a triangulated category C. We show that the projective dimension of Hom(-,X)|T is at most one if and only if there are no non-zero morphisms between objects in T[1] factoring through X, when the object X belongs to a suitable subcategory of C. As a consequence, we obtain a characterisation of the objects of infinite projective dimension in the category of finitely presented contravariant functors on a cluster-tilting subcategory of C.

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