I am reading this this entry http://stacks.math.columbia.edu/tag/06XU of the Stacks Project.
I'm having problems in understanding how $\left(L^{-i+1}\oplus A\right) / L^{-i}$ is constructed. I mean, which map are we using to construct the cokernel?
I guess $f$ should be used in the proof but they don't mention anything.