Subject: categories: ramifications of Goldblatt's notion of a skeleton of a category

From: "Galchin Vasili" <[email-masked]>
Date: Thu, 29 Jun 2006 00:29:09 -0500

Hello,

     Rob Goldblatt in section 9.2 of his book "Topoi: The Categorical
Analysis of
Logic" introduces the notion of a "skeleton of a category C" which he
defines as a "full
subcategory C-sub-zero of C that is skeletal, and such that each C-object is
isomorphic
to one and only one C-sub-zero object". This statement seems to imply that
we can have an "operator":

   skel: CAT -> CAT   where CAT is the categories of (small) categories

such that

  1) skel is idempotent on any member of C of CAT, i.e.
]
  skel (skel (C)) = skel (C)

  2) skel (C) = a "maximal" skeleton of C.

I am struggling with

   1) what "maximal" means in this case? E.g. is there some kind of order on
all the
           skeletons of category C?

   2) would the "operator" skel be a functor?

Kind regards, Bill Halchin