Width and Local Homology Dimension for Triangulated Categories

Li Wang ()
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Li Wang: Department of Mathematics, Lanzhou City University, Lanzhou 730070, China

Mathematics, 2024, vol. 12, issue 17, 1-11

Abstract: Let T be a compactly generated triangulated category. In this paper, the width and local homology dimension of an object X with respect to a homogeneous ideal a , width R ( a , X ) and hd ( a , X ) , respectively, are introduced. The local nature and some basic properties of width R ( a , X ) and hd ( a , X ) are provided. In addition, we give an upper bound and lower bound of width R ( a , X ) . What is more, we give the relationship between the local homology dimension hd ( a , X ) and the arithmetic rank of a and dim R .

Keywords: triangulated category; width; local homology dimension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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