Auslander-Reiten Translations in Monomorphism Categories
Auslander-Reiten Translations in Monomorphism Categories
Auslander-Reiten Translations in Monomorphism Categories
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The functor: Mono<br />
Mono : Morn(A) −→ Sn(A),<br />
⎛<br />
⎜<br />
⎝<br />
X1<br />
X2<br />
.<br />
Xn−1<br />
Xn<br />
⎞<br />
⎟<br />
⎠<br />
(φ i )<br />
⎛<br />
⎜<br />
↦→ ⎜<br />
⎝<br />
X1<br />
Im φ1<br />
.<br />
Im(φ1···φn−2)<br />
Im(φ1···φn−1)<br />
where φ ′ i : Im(φ1 · · · φ i) ↩→ Im(φ1 · · · φ i−1), 2 ≤ i ≤ n − 1, and<br />
φ ′ 1 : Im φ1 ↩→ X1 are the canonical monomorphisms.<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 7 / 24<br />
⎞<br />
⎟<br />
⎠<br />
(φ ′ i )<br />
,