Two more responses on the lim-1 question.......DMD
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Subject: Re: history of lim-1
Date: Wed, 18 Jul 2001 22:41:21 -0500
From: Clarence Wilkerson <wilker@math.purdue.edu>

I recall a paper by a student of Milnor's, R. Yee (sic)
used to be the reference. I think this included the case
of larger towers as well. Yee was a faculty member at the
U. of Hawaii when I was there.

Clarence Wilkerson
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Subject: Re: responses to lim-1
Date: Wed, 18 Jul 2001 16:33:02 -0400 (EDT)
From: Claude Schochet <claude@mersenne.math.wayne.edu>

It is certainly the case that Steenrod was the first to calculate a
non-trivial lim^1. Jerry Kaminker and I wrote about "generalized Steenrod
homology theories" with this in mind. It was a very specific computation,
meant to illustrate the difference between Cech homology and Steenrod
homology. However, there is no sign in that paper of lim^1 being a derived
functor of lim (the right words hadn't even been invented yet) nor is
there any systematic treatment. It is simply an obstruction group.

Milnor's 1961 paper deals with Steenrod's theory, and he produces a short
exact sequence to compute H_*(inverse limit of X_i$ where the X_i are
finite complexes and X = inverse limit X_i is a compact metric space.
This of course involves lim and lim^1.
(For some years Jerry  and I had the only copies of this paper and
were the "publishers", so to speak.)  There is no mention of the 6 term
sequence there.

Milnor's Pacific J. paper (1962) that is most familiar to topologists
deals with the dual situation - computing h^*(infinite CW cx) in terms of
the finite subcomplexes.

So I believe that Brayton is correct - Roos gets credit for the 6 term
sequence for abelian groups.

Thanks!