Auslander-Reiten Translations in Monomorphism Categories
Auslander-Reiten Translations in Monomorphism Categories
Auslander-Reiten Translations in Monomorphism Categories
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The notions<br />
A: an Art<strong>in</strong> algebra, A-mod: the category of all f<strong>in</strong>. gen. left A-modules<br />
Morn(A): the morphism category<br />
�<br />
of A-mod, n ≥ 2<br />
Objects: X (φi ) =<br />
Xn<br />
� X1<br />
.<br />
Xn<br />
(φ i )<br />
φn−1 ��<br />
Xn−1<br />
, φ i : X i+1 → X i are A-maps, i.e.<br />
φn−2 ��<br />
· · ·<br />
φ2 ��<br />
X2<br />
φ1 ��<br />
X1<br />
Bao-L<strong>in</strong> Xiong (SJTU) <strong>Auslander</strong>-<strong>Reiten</strong> <strong>Translations</strong> <strong>in</strong> <strong>Monomorphism</strong> <strong>Categories</strong> ISPN ’80 3 / 24