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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next 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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