Remark 90.2.8. Observe that in the situation of Lemma 90.2.7 we have

The first equality by More on Algebra, Lemma 15.60.3 and the second by More on Algebra, Lemma 15.85.1. We have maps of complexes

which is close to being a distinguished triangle, see Algebra, Lemma 10.134.4. If it were a distinguished triangle we would conclude that the image of $\xi $ in $\mathop{\mathrm{Ext}}\nolimits ^2_ B(\mathop{N\! L}\nolimits _{B/A}, N)$ would be the obstruction to the existence of a solution to (90.2.0.1).

## Comments (0)