A slightly more recent exposition is given in D. A. Edwards and H. M. Hastings, Cech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Mathematics 542, Springer, 1976 on pages 6--7. It is a bit strange that Edwards and Hastings credit Mardesic and do not mention Deligne. Understandably, they must have been more familiar with the literature on shape theory than on algebraic geometry. Dan Isaksen University of Notre Dame isaksen.1@nd.edu
Date: Thu, 31 May 2001 07:42:43 -0400 From: William Boshuck <boshuk@triples.math.mcgill.ca> To: categories@mta.ca Subject: categories: Re: Pro C
This is due to Deligne, and can be found towards the beginning of SGA4, Expose I, section 8. I would like to know of a more recent source that is so (or more) thorough on the subject. cheers, -b On Tue, May 29, 2001 at 09:38:43PM -0700, Bill Rowan wrote:
I have read that if C is a category, and the axiom of choice is assumed, then Pro C is equivalent to its full subcategory of diagrams where the diagram category is an inversely-directed set. Does anyone know where this is proved in the literature?
Thanks,
Bill Rowan