• Resolution using T-branes

I thought I knew it, but I don't, even for one strands, no disks. Is it because of the chain complex vs cohomology, or some other weird sign error?

Can we do something easier and almost trivial? For example, braiding a bunch of punctures on $\R$? Do we know how it works? OK, there, it should work. Because we have puncture, and there is no dots.

Suppose we have an infinite array of puntures. I have a vertical line between puncture $-1/2$ and $1/2$, and I braid the two punctures positively. Then, I would have a line running downward. I have

$$ T_{-1} \to T_0[-1] \gets T_{1 $$