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arXiv · 1111.3077

Projective Dimensions in Cluster-Tilted Categories

Alex Lasnier
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Abstract

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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BibTeXRIS

Alex Lasnier. 2011-11-13. Projective Dimensions in Cluster-Tilted Categories. https://arxiv.org/abs/1111.3077

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