  We develop a new approach to highest weight categories $\cal{C}$ with good
(and cogood) posets of weights via pseudocompact algebras by introducing
ascending (and descending) quasi-hereditary pseudocompact algebras. For
$\cal{C}$ admitting a Chevalley duality, we define and investigate tilting
modules and Ringel duals of the corresponding pseudocompact algebras. Finally,
we illustrate all these concepts on an explicit example of the general linear
supergroup $GL(1|1)$.

Rings and Algebras;Representation Theory