In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...

BACKGROUND AND AIMS The root meristem of the Arabidopsis thaliana mature embryo is a highly organized structure in which individual cell shape and size must be regulated in co-ordination with the surrounding cells. The objective of this study was to determine the role of the AUX1 LAX family of auxin import carriers during the establishment of the embryonic root cell pattern. METHODS The radic...

Binary logical relations do not compose. So we generalise the notion of logical relation to one of lax logical relation, so that binary lax logical relations do compose. We give both a direct generalisation and a corresponding category theoretic formulation. We generalise the Basic Lemma for logical relations to a Basic Lemma for lax logical relations. Finally, we give an axiomatic category the...

The notion of geometric nerve of a 2-category (Street, [18]) provides a full and faithful functor if regarded as defined on the category of 2-categories and lax 2-functors. Furthermore, lax 2-natural transformations between lax 2-functors give rise to homotopies between the corresponding sim-plicial maps. These facts allow us to prove a representation theorem of the general non abelian cohomolo...

The category of Set-valued presheaves on a small category B is a topos. Replacing Set by a bicategory S whose objects are sets and morphisms are spans, relations, or partial maps, we consider a category Lax(B,S) of S-valued lax functors on B. When S = Span, the resulting category is equivalent to Cat/B, and hence, is rarely even cartesian closed. Restricting this equivalence gives rise to expon...

In this paper, numerical investigation of upward two phase flow of air-water has been studied. Different conditions of flow regimes including annular, wispy annular, slug, churn and bubbly are simulated based on Hewitt and Roberts map, and a good agreement between the experimental data of the map and the numerical simulation has been observed. Accordingly, a proper CFD model in CFD software of ...