An extriangulated functor from (n+1)-term subcategories to (n+1)-term complexes is constructed, with equivalent conditions for fullness yielding an extriangle equivalence and a mutation-compatible silting bijection.
Extriangulated ideal quotients, with applications to cluster theory and gentle algebras.arXiv preprint arXiv:2308.05524
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abstract
We extend results of Br\"ustle-Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpretation of such quotients: they appear as prototypical examples of a new construction of quotients of extriangulated categories by ideals generated by morphisms from injectives to projectives. We apply our results to Frobenius exact cluster categories and Higgs categories with suitable relative extriangulated structures, and to categories of walks related to gentle algebras. In all three cases, the extriangulated structures are well-behaved (they are 0-Auslander) and their quotients are equivalent to homotopy categories of two-term complexes of projectives over suitable finite-dimensional algebras.
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math.RT 4years
2026 4representative citing papers
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Introduces presilting sequences in 0-Auslander extriangulated categories with a bijection to tau-exceptional sequences and defines a new tau-cluster morphism category M(C).
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