  We apply the notion of a full convex subcategory to a wide range of algebras
including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura,
simply connected, strongly simply connected, left supported, and
cluster-tilted. In particular, given an algebra $\Lambda$ from one of the
aforementioned classes, we investigate certain factor algebras $\Lambda/I$
where $I$ is an ideal generated by a suitable idempotent.
