Auslander-Reiten Translations in Monomorphism Categories
Auslander-Reiten Translations in Monomorphism Categories
Auslander-Reiten Translations in Monomorphism Categories
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
The kernel and cokernel functors<br />
Ker : 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 />
Xn<br />
Ker(φ1···φn−1)<br />
.<br />
Ker(φn−2φn−1)<br />
Ker φn−1<br />
where φ ′ i : Ker(φ i · · · φn−1) ↩→ Ker(φ i−1 · · · φn−1), 2 ≤ i ≤ n − 1, and<br />
φ ′ 1 : Ker(φ1 · · · φn−1) ↩→ Xn 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 5 / 24<br />
⎞<br />
⎟<br />
⎠<br />
(φ ′ i )<br />
,
Change language