Term used in spectral sequences

Term used in spectral sequences

[Michael Barr]

As some of you know, my wife and I are translating Grothendieck's
Tohoku paper.  Originally, it was suggested that it be published as a
TAC reprint, but Grothendieck refuses permission because he "does not
believe in copyright".  So I thought to retype it and post it on my own
site (so sue).   I then realized that translation would be easier than
retyping.

Which brings me to a translation problem.  I am not expert in spectral
sequences and what I know is from Cartan-Eilenberg.  I cannot related
G's definition to theirs.  G defines a spectral sequence as a pair
E=(E^{p,q}_r,E^n), all indexed objects of an abelian category subject to
five conditions.  The first three refer only to the E^{p,q}_r, including
that for each pair p,q the E^{p,q}_r stabilize vis-vis r to a term he
calls E^{p,q}_\infty (and not E^{p,q}).  The fourth assumes
"isomorphisms $\beta^{p,q}:E^{pq}\to G^p(E^{p+q})$.  The family $(E^n)$
without filtrations is called the \emph{l'aboutissement} of the spectral
sequence $E$."  The E^n are assumed filtered and G^p is the associated
grading:  G^p(A)=F^p(A)/F^{p-1}(A).  Now this makes no sense.  The only
thing called E^{pq} would be the term E^n for n=pq and this is really
unlikely.  I strongly suspect the domain of \beta^{p,q} is intended to
be E^{p,q}_\infty.  Finally does anyone have any idea how
"aboutissement" is to be translated.  It means something like limit, but
the usual term for that is of course "limite".  The Cartan-Eilenberg
development is different enough that there seems not to be any
corresponding word.

Michael