Suppose I have a smooth projective variety $X$, and a semi-orthogonal decomposition of its bounded derived category:


$$D^b(X)= < A, E\_1, E\_2, ... , E\_n >$$


where the $E\_i$ are fully faithful, saturated (and hence admissible) subcats of $D^b(X)$. Is A authomatically saturated/admissible? Why? If not, under what assuptions?



is the orthogonal complement of a saturated sequence saturated?
Yes, it is. See Bondal, A. I.; Kapranov, M. M. Representable functors, Serre functors, and reconstructions. 


