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From: "Fred E.J. Linton" <fejlinton@usa.net>
To: "Ellis D. Cooper" <xtalv1@netropolis.net>, <categories@mta.ca>
Subject: Re: Subobject Classifier Algorithm
Date: Thu, 24 Feb 2011 17:14:44 -0500	[thread overview]
Message-ID: <E1PsowU-00036q-TT@mlist.mta.ca> (raw)

When "Ellis D. Cooper" <xtalv1@netropolis.net> asks,

> What are the general rules for calculating the sub-object classifier
> of a topos? Or, for what class of toposes is there an algorithm for
> calculating the sub-object classifier of its members?

I imagine the sort of response he hoped for is one like:

In a presheaf topos, the suboject classifier &Omega; can be unraveled,
from its universal property, by help of the Yoneda Lemma, as each of the 
various values &Omega;(X) that &Omega; must take at an object X "is" the 
set of natural transformations from hom(-, X) to &Omega;, which, in turn,  
"is" the set of subfunctors of the representable functor hom(-, X).

I'll let others formulate similarly "algorhythmic" proposals for 
other sorts of topoi (comonadic ones, sheaves, etc.).

Cheers, -- Fred



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             reply	other threads:[~2011-02-24 22:14 UTC|newest]

Thread overview: 10+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2011-02-24 22:14 Fred E.J. Linton [this message]
  -- strict thread matches above, loose matches on Subject: below --
2013-10-20  8:25 Subobject classifier algorithm Venkata Rayudu Posina
2013-10-23  9:52 ` Prof. Peter Johnstone
2011-03-03 15:17 Subobject Classifier Algorithm Ellis D. Cooper
2011-03-04 13:44 ` Eduardo J. Dubuc
2011-02-23 15:16 Ellis D. Cooper
2011-02-24 17:11 ` F. William Lawvere
2011-02-25 11:20 ` Paul Taylor
2011-03-01 16:52   ` F. William Lawvere
2011-03-02 10:35     ` Paul Taylor

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