First we shall give an overview on the main geometrical aspects
of the study of residuated lattices; a powerful method which has
been introduced by the speaker.

Next, to show an application we present the structural
description of both involutive uninorms and finite involutive
uninorm chains. This description involves a striking new
construction, called skew-symmetrization, in which one has to
leave the accustomed residuated setting, and has to enter a co-
residuated setting too.

So, for the description of residuated structures one needs as
well co-residuation; it is a never expected surpising
observation in the theory of residuated lattices; a theory which
goes back to 70 years.

We shall explain how the geometric approach makes the finding of
this observation, the finding and the prooving of the structural
description of involutive uninorms a piece of cake.