Date: Mon, 20 Sep 1999 12:06:05 -0500 (CDT)
From: Hongseok Yang <hyang@cs.uiuc.edu>
Subject: categories: Skeleton of a category

Would you let me know when the category has an equivalent skeleton? (The 
definition of the skeleton subcategory that I have in mind is from
MacLane p91: a full subcategory such that for any object in the original 
category, there exists a unique isomorphic object in the
skeleton subcategory.) My question is mainly about when I can use the
choice axiom without causing contradiction. For instance, I heard that the
category of abelian groups doesn't have an equivalent skeleton
subcategory.

Thank you very much,
Hongseok


Date: Mon, 20 Sep 1999 18:44:56 +0100 (BST)
From: Paul Taylor <pt@dcs.qmw.ac.uk>
Subject: categories: Re: Skeleton of a category

> Would you let me know when the category has an equivalent skeleton?

"every small category has a skeleton"  iff  the axiom of choice holds.

See Exercise 3.26 in my book, or
	http://www.dcs.qmw.ac.uk/~pt/book/html/s3e.html#e3.26
for a preorder example.

Exercise 4.37 defines "skeletal"
	http://www.dcs.qmw.ac.uk/~pt/book/html/s4e.html#e4.37

Paul