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From: Rory Lucyshyn-Wright <rorylw@mathstat.yorku.ca>
To: <categories@mta.ca>
Subject: Totally distributive toposes
Date: Mon, 12 Sep 2011 20:46:47 -0400	[thread overview]
Message-ID: <E1R3cwf-0007xD-TR@mlist.mta.ca> (raw)

My preprint "Totally distributive toposes" (http://arxiv.org/abs/1108.4032)
has been updated to include an extended result, namely that the lex 
totally distributive categories with a small set of generators are exactly 
the injective Grothendieck toposes.

Regards,
Rory Lucyshyn-Wright

Abstract:  A locally small category E is totally distributive (as defined 
by Rosebrugh-Wood) if there exists a string of adjoint functors t -| c -| 
y, where y : E --> E^ is the Yoneda embedding. Saying that E is lex 
totally distributive if, moreover, the left adjoint t preserves finite 
limits, we show that the lex totally distributive categories with a small 
set of generators are exactly the injective Grothendieck toposes, studied 
by Johnstone and Joyal. We characterize the totally distributive 
categories with a small set of generators as exactly the essential 
subtoposes of presheaf toposes, studied by Kelly-Lawvere and 
Kennett-Riehl-Roy-Zaks.




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             reply	other threads:[~2011-09-13  0:46 UTC|newest]

Thread overview: 2+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2011-09-13  0:46 Rory Lucyshyn-Wright [this message]
  -- strict thread matches above, loose matches on Subject: below --
2011-09-02  4:08 Rory Lucyshyn-Wright

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