Auslander–Reiten theory in extriangulated categories
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Publication:6151517
DOI10.1090/btran/159arXiv1805.03776MaRDI QIDQ6151517
Hiroyuki Nakaoka, Yann Palu, Osamu Iyama
Publication date: 12 February 2024
Published in: Transactions of the American Mathematical Society, Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.03776
triangulated categoriesexact categoriesAuslander-Reiten theoryextriangulated categoriesAuslander-Reiten-Serre duality
Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Cohen-Macaulay modules in associative algebras (16G50) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Abelian categories, Grothendieck categories (18E10)
Cites Work
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- Graded quiver varieties and derived categories
- Auslander-Reiten theory in a Krull-Schmidt category
- 0-Calabi-Yau configurations and finite Auslander-Reiten quivers of Gorenstein orders
- Almost split sequences in dimension two
- A characterization of finite Auslander-Reiten quivers
- Radical layers of representable functors
- \(\tau\)-categories. III: Auslander orders and Auslander-Reiten quivers.
- \(n\)-exangulated categories (I): definitions and fundamental properties
- Families of Auslander-Reiten components for simply connected differential graded algebras.
- Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
- Auslander correspondence.
- Extensions of covariantly finite subcategories
- Duality for derived categories and cotilting bimodules
- Algebren, Darstellungsköcher, Überlagerungen und zurück
- Almost split sequences in subcategories
- Covering spaces in representation-theory
- Perpendicular categories with applications to representations and sheaves
- Algebra VIII: Representations of finite-dimensional algebras. Transl. from the Russian
- Approximations and almost split sequences in homologically finite subcategories
- Auslander-Reiten theory over topological spaces
- Auslander-Reiten theory via Brown representability
- Classifications of exact structures and Cohen-Macaulay-finite algebras
- Triangulated quotient categories revisited
- Phantom ideals and cotorsion pairs in extriangulated categories
- Triads.
- Applications of contravariantly finite subcategories
- Stable equivalence of dualizing R-varieties
- Relative homological algebra and purity in triangulated categories
- Cohen-Macaulay differential graded modules and negative Calabi-Yau configurations
- \(n\)-exangulated categories (II): constructions from \(n\)-cluster tilting subcategories
- Almost split sequences in tri-exact categories
- The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
- Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories
- Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories
- Hearts of twin cotorsion pairs on extriangulated categories
- Desingularizations of quiver Grassmannians via graded quiver varieties
- \(\tau\)-categories. I: Ladders.
- The category of lattices over a lattice-finite ring.
- On triangulated orbit categories
- Almost split sequences and approximations
- \(\tau\)-categories. II: Nakayama pairs and rejective subcategories.
- Noetherian hereditary abelian categories satisfying Serre duality
- Introduction to τ-tilting theory
- Relative homology and representation theory 1
- The homological theory of maximal Cohen-Macaulay approximations
- Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras
- Hammocks
- Two-dimensional tame and maximal orders of finite representation type
- Auslander-Reiten Triangles in Derived Categories of Finite-Dimensional Algebras
- Representation theory of artin algebras iii almost split sequences
- Almost split sequences for integral group rings and orders
- Representation theory of artin algebras IV1)Invariants given by almost split sequences
- Exact categories and vector space categories
- Deriving DG categories
- The generalized Auslander–Reiten duality on an exact category
- Representation Theory of Artin Algebras II
- The relationship between homological properties and representation theoretic realization of artin algebras
- Non-kissing complexes and tau-tilting for gentle algebras
- Auslander-Reiten triangles in subcategories
- -tilting theory
