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0-Auslander correspondence

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arxiv 2306.15958 v2 pith:7HZGQIZ7 submitted 2023-06-28 math.RT math.CT

0-Auslander correspondence

classification math.RT math.CT
keywords auslandercorrespondenceanaloguecategoriescategoryexactgorsky--nakaoka--palunote
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this short note we prove an analogue of Auslander correspondence for exact dg categories whose $H^0$-category is $0$-Auslander in the sense of Gorsky--Nakaoka--Palu.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. From $(n+1)$-term subcategories to $(n+1)$-term complexes

    math.RT 2026-07 accept novelty 7.0

    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.

  2. Relations between categorifications of higher-dimensional type $A$ cluster combinatorics

    math.RT 2026-05 unverdicted novelty 7.0

    In higher Auslander algebras of type A, the d-almost positive subcategory is the d-exangulated quotient of the d-exact subcategory of the module category and the (d+2)-angulated cluster category by ideals from injecti...

  3. Extriangulated ideal quotients and $d$-Auslander categories

    math.RT 2026-07 accept novelty 6.0

    An algebraic d-Auslander extriangulated category satisfying a vanishing condition admits an extriangulated ideal quotient equivalent to a truncated homotopy category of complexes.

  4. From objects finitely presented by a rigid object in a triangulated category to 2-term complexes

    math.RT 2025-09 accept novelty 6.0

    For a rigid object M, the presentation functor P from pr(M) to 2-term complexes over End(M) is full, dense, detects extriangles, and induces a mutation-commuting bijection between basic relative cluster-tilting object...