Monads in Double Categories

We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and define what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.Comment: 30 pages; v2: accepted for publication in the Journal of Pure and Applied Algebra; added hypothesis in Theorem 3.7 that source and target functors preserve equalizers; on page 18, bottom, in the statement concerning the existence of a left adjoint, "if and only if" was replaced by "a sufficient condition"; acknowledgements expande

Double Adjunctions and Free Monads

We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg--Moore objects in double categories. We improve upon our earlier result in "Monads in Double Categories", JPAA 215:6, pages 1174-1197, 2011, to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category. We also prove that a double category admits Eilenberg--Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double-categorical Yoneda Lemma.Comment: 52 page

Exterior power operations on higher K-groups via binary complexes

We use Grayson's binary multicomplex presentation of algebraic K-theory to give a new construction of exterior power operations on the higher K-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a lambda-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial functors is the universal lambda-ring on one generator

Chemo-mechanics of salt and ice crystallization in rocks : a 4D study using X-ray micro computed tomography

COMInternational audienc

Considering the need for alternative intervention strategies for the management of diabetic policy formulation in South Africa

CITATION: Thomas, V. V., De Kock, I. H. & Bam, L. 2018. Considering the need for alternative intervention strategies for the management of diabetic policy formulation in South Africa. In SAIIE29 Proceedings, 24-26 October 2018, Spier, Stellenbosch, South Africa.The original publication is available at https://conferences.sun.ac.za/index.php/saiie29/saiie29/schedConf/presentationsENGLISH ABSTRACT: The increasing prevalence of diabetes in South Africa, alongside other non-communicable diseases, places a heavy burden on the health care system; especially when faced with the significant difference in quality of care between private and public health care, and the increased burden of disease. This paper analyses various diabetic policies already implemented in South Africa, and considers the need to investigate alternative policies and intervention strategies to manage diabetes in South Africa. Due to the complex nature and non-linear interactions which exist within the health care system, a system dynamics-based approach is suggested as a useful analysis tool to evaluate and understand the dominant factors that influence the effective management of diabetes to potentially inform more effective and efficient diabetic policy formulation.https://conferences.sun.ac.za/index.php/saiie29/saiie29/paper/view/3590Publisher's versio

Pore-scale freeze-thaw experiments with environmental micro-CT

AFFInternational audienc

3D imaging of clay minerals inside sandstone: pushing the spatial resolution limits using ptychographic tomography

Characterization of microporous, clay-sized particles in natural stone is essential for the understanding of their dynamics. These processes are importand in the fields of oil and gas, groundwater, building stone weathering and soil science. Methods such as X-ray micro-computed tomography is an excellent tool to study features larger than or just under 1 μm, but below the 400 nm limit, the technique falls short. Although destructive methods exists (e.g. FIB/SEM), non-destructive imaging at these very high resolutions has been impossible, until recent developments at synchrotron beam lines. In this study, we use ptychographic tomography at the cSAXS beam line of the PSI in Switzerland, for imaging of clay microstructure at resolutions down to 45 nm, which is the first application of ptychographic tomography for geological samples to our knowledge. During these experiments, relative humidity of the sample’s environment was controlled, in order to asses the influence of R.H. on the analyzed clay minerals. Based on these images, quantitative data on mineral content, porosity, connectivity and behavior under changing environmental conditions of clay mineral clusters was acquired