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Boundedness And Complete Distributivity
 IV, Appl. Categ. Structures
"... . We extend the concept of constructive complete distributivity so as to make it applicable to ordered sets admitting merely bounded suprema. The KZdoctrine for bounded suprema is of some independent interest and a few results about it are given. The 2category of ordered sets admitting bounded ..."
Abstract

Cited by 16 (7 self)
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. We extend the concept of constructive complete distributivity so as to make it applicable to ordered sets admitting merely bounded suprema. The KZdoctrine for bounded suprema is of some independent interest and a few results about it are given. The 2category of ordered sets admitting bounded suprema over which nonempty infima distribute is shown to be biequivalent to a 2category defined in terms of idempotent relations. As a corollary we obtain a simple construction of the nonnegative reals. 1. Introduction 1.1. The main theorem of [RW1] exhibited a biequivalence between the 2category of (constructively) completely distributive lattices and suppreserving arrows, and the idempotent splitting completion of the 2category of relations  relative to any base topos. Somewhat in passing in [RW1], it was pointed out that this biequivalence provides a simple construction of the closed unit interval ([0; 1]; ), namely as the ordered set of downsets for the idempotent relat...
The low dimensional structures that tricategories form, preprint http://arxiv.org/abs/0711.1761
, 2007
"... We form tricategories and the homomorphisms between them into a bicategory. We then enrich this bicategory into an example of a threedimensional structure called a locally double bicategory, this being a bicategory enriched in the monoidal 2category of weak double categories. Finally, we show that ..."
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Cited by 3 (0 self)
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We form tricategories and the homomorphisms between them into a bicategory. We then enrich this bicategory into an example of a threedimensional structure called a locally double bicategory, this being a bicategory enriched in the monoidal 2category of weak double categories. Finally, we show that every sufficiently wellbehaved locally double bicategory gives rise to a tricategory, and thereby deduce the existence of a tricategory of tricategories. 1