* Preprint: Totally distributive categories and injective toposes
@ 2011-08-22 2:16 Rory Lucyshyn-Wright
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From: Rory Lucyshyn-Wright @ 2011-08-22 2:16 UTC (permalink / raw)
To: categories
A preprint of my paper "Totally distributive categories and injective
toposes" is now available at
http://arxiv.org/abs/1108.4032
This paper subsumes the content of talks that I gave in Halifax and
Schenectady. An abstract is included below.
Your comments are welcome.
Regards,
Rory Lucyshyn-Wright
Abstract: We establish a connection between the totally distributive
categories, studied by Marmolejo, Rosebrugh, and Wood, and the injective
and quasi-injective Grothendieck toposes, studied by Johnstone and Joyal.
We show that every quasi-injective topos is totally distributive and that
every injective topos is lex totally distributive. As a partial converse,
we show that every lex totally distributive category with a small dense
generator is a quasi-injective topos. In view of work of Johnstone-Joyal
relating injective and quasi-injective toposes to continuous categories,
our results provide partial analogues of the dual equivalence between
continuous dcpos and completely distributive lattices (Hoffmann, Lawson)
and its restriction to continuous lattices (Banaschewski).
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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2011-08-22 2:16 Preprint: Totally distributive categories and injective toposes Rory Lucyshyn-Wright
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