The magnitude of a module category equals the Euler characteristic of its Auslander–Reiten quiver; for biserial algebras it equals the rank, and for hereditary type A_n it equals n.
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An algebraic d-Auslander extriangulated category satisfying a vanishing condition admits an extriangulated ideal quotient equivalent to a truncated homotopy category of complexes.
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Magnitude of module categories
The magnitude of a module category equals the Euler characteristic of its Auslander–Reiten quiver; for biserial algebras it equals the rank, and for hereditary type A_n it equals n.
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Extriangulated ideal quotients and $d$-Auslander categories
An algebraic d-Auslander extriangulated category satisfying a vanishing condition admits an extriangulated ideal quotient equivalent to a truncated homotopy category of complexes.