Mea culpa

Mea culpa

[Michael Barr]

As I was preparing a paper based on the talk I gave in Vancouver on a 
simplicial acyclic models theorem, I realized that the argument I gave was 
flawed.  I had asserted that a certain square commuted by naturality. 
Suffice it to say it didn't.  The result, which I have examined very 
closely in the special case of a standard resolution by a cotriple, just 
does not seem true.  The problem comes from the commuting of s^0.  It 
might seem that that means only failure of commutation with s^0, but that 
is the base of an induction and I must conclude that none of degeneracies 
work.  Thus I have not advanced in any way on Kleisli's 1974 paper which 
is an acyclic models theorem for semi-simplicial complexes.

Given that there were at least two talks on duality at the meeting, what I 
should have spoken on was my paper on Topological *-autonomous categories, 
revisited.  It can be found on my web site http://www.math.mcgill.ca/barr/ 
as the most recent paper. It corrects, fills in the gaps of and adds some 
new material to my 2006 paper found in TAC, 2006.

Michael


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