Abstract
In this series of papers, we introduce τ-categories, which are additive categories with some kind of Auslander–Reiten sequences. We apply them to study the category of lattices over orders. In this first paper, we study minimal projective resolutions in functor categories over τ-categories. Then we give a structure theorem of completely graded τ-categories using mesh categories.
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Mathematics Subject Classifications (2000)
primary 16G30; secondary 16E65, 16G70, 18E05.
Osamu Iyama: Current address: Department of Mathematics, University of Hyogo, Himeji, 671-2201, Japan. e-mail: iyama@sci.u-hyogo.ac.jp.
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Iyama, O. τ-Categories I: Ladders. Algebr Represent Theor 8, 297–321 (2005). https://doi.org/10.1007/s10468-005-0968-5
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DOI: https://doi.org/10.1007/s10468-005-0968-5