From: "Galchin Vasili" <vigalchin@gmail.com>
To: categories@mta.ca
Subject: ramifications of Goldblatt's notion of a skeleton of a category
Date: Thu, 29 Jun 2006 00:29:09 -0500 [thread overview]
Message-ID: <E1Fwnu8-0004Wm-8s@mailserv.mta.ca> (raw)
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
next reply other threads:[~2006-06-29 5:29 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2006-06-29 5:29 Galchin Vasili [this message]
2006-07-01 23:14 Fred E.J. Linton
2006-07-03 11:07 Ronnie Brown
2006-07-04 16:14 Bruce Bartlett
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