From: Ronald Brown <ronnie@ll319dg.fsnet.co.uk>
To: categories@mta.ca (categories)
Subject: Re: chain complexes: in reply to John Baez
Date: Sun, 20 Jul 2003 17:43:55 +0100 [thread overview]
Message-ID: <5.0.2.1.0.20030720173046.00a8aec0@pop.freeserve.com> (raw)
In-Reply-To: <200307140729.h6E7TUn18042@math-cl-n01.ucr.edu>
reply to r.brown@bangor.ac.uk
The paper
(R. BROWN and HIGGINS, P.J.), `Cubical abelian groups with
connections are equivalent to chain complexes', Homology, Homotopy
and Applications, 5(1) (2003) 49-52.
has a reference to Grothendieck's `cat\'egorie
cofibr\'ee....' (1968) SLNM 79, (the canonical reference for the first
question),
and also to Bourn (JPAA 1990), and gives a proof that 5 different
structures are, in an additive category with kernels, equivalent to chain
complexes. Among these structures is strict globular omega-categories.
However, this is deduced from some non abelian and more difficult results.
Ronnie Brown
Dear Categorists -
Who first showed that an internal category in
the category of abelian groups was a 2-term chain
complex of abelian groups? What's a good reference?
Who first showed that an internal strict omega-category
in the category of abelian groups was a chain complex
of abelian groups? What's a good reference?
(Of course for "internal X in the category of Y's",
I am willing to accept "internal Y in the category of X's"
as a substitute.)
Best,
jb
prev parent reply other threads:[~2003-07-20 16:43 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-07-14 7:29 chain complexes John Baez
2003-07-20 16:43 ` Ronald Brown [this message]
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