* Totally distributive toposes
@ 2011-09-02 4:08 Rory Lucyshyn-Wright
0 siblings, 0 replies; 2+ messages in thread
From: Rory Lucyshyn-Wright @ 2011-09-02 4:08 UTC (permalink / raw)
To: categories
My preprint "Totally distributive toposes" (http://arxiv.org/abs/1108.4032)
has been updated to include an additional corollary, namely that the
totally distributive categories with a small set of generators are exactly
the essential subtoposes of presheaf toposes [C^op, Set], which were shown
by Kelly-Lawvere to correspond to idempotent ideals in the small category
C. Some minor additional changes have been made, and the title has
changed.
Regards,
Rory
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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* Totally distributive toposes
@ 2011-09-13 0:46 Rory Lucyshyn-Wright
0 siblings, 0 replies; 2+ messages in thread
From: Rory Lucyshyn-Wright @ 2011-09-13 0:46 UTC (permalink / raw)
To: categories
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.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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