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On wide subcategories

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CAR - Cluster algebras and representation theory

In earlier joint work with Marsh, we defined a categorical structure on the set of all wide subcategories of a fixed module category, where maps correspond to tau-rigid objects. Our construction worked for tau-tilting finite algebras, and was motivated by Igusa-Todorov’s definition of such a category in the hereditary case. In recent joint work with Hanson, we considered the case of general finite-dimensional algebras. One then needs to restrict to a certain subclass of functorially finite subcategories; the tau-perpendicular wide categories. These were introduced by Jasso, generalizing Geigle-Lenzing perpendicular categories in the hereditary setting. We give a characterize such categories, inspired by the work of Marks-Stoviceck and Ingalls-Thomas, which provided links to torsion theory.

This talk is part of the Isaac Newton Institute Seminar Series series.

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