  One of the aims of this paper is to better explain the philosophy behind the
computations in [E.Bifet, C.De Concini,C.Procesi Cohomology of Regular
Embeddings ] and to place them in a wider conceptual setting. Another aim of
the paper is to outline in the last section an ``equivariant'' approach to some
key results in the theory of toric varieties. The text of the first three
sections follows closely a talk delivered at the University of Copenhagen in
July 1989 on the occasion of the Zeuthen Symposium. This paper is dedicated to
the memory of my friend Pere Menal and will appear in the Fall 1992 issue,
dedicated to his memory, of Publicacions Matem\`atiques, Universitat Aut\`onoma
de Barcelona.
