A comparison theorem for simplicial resolutions

It is well known that Barr and Beck's definition of comonadic homology makes sense also with a functor of coefficients taking values in a semi-abelian category instead of an abelian one. The question arises whether such a homology theory has the same convenient properties as in the abelian case. Here we focus on independence of the chosen comonad: conditions for homology to depend on the induced class of projectives only.Comment: 16 page

Three viewpoints on semi-abelian homology

The main theme of the thesis is to present and compare three different viewpoints on semi-abelian homology, resulting in three ways of defining and calculating homology objects. Any two of these three homology theories coincide whenever they are both defined, but having these different approaches available makes it possible to choose the most appropriate one in any given situation, and their respective strengths complement each other to give powerful homological tools. The oldest viewpoint, which is borrowed from the abelian context where it was introduced by Barr and Beck, is comonadic homology, generating projective simplicial resolutions in a functorial way. This concept only works in monadic semi-abelian categories, such as semi-abelian varieties, including the categories of groups and Lie algebras. Comonadic homology can be viewed not only as a functor in the first entry, giving homology of objects for a particular choice of coefficients, but also as a functor in the second variable, varying the coefficients themselves. As such it has certain universality properties which single it out amongst theories of a similar kind. This is well-known in the setting of abelian categories, but here we extend this result to our semi-abelian context. Fixing the choice of coefficients again, the question naturally arises of how the homology theory depends on the chosen comonad. Again it is well-known in the abelian case that the theory only depends on the projective class which the comonad generates. We extend this to the semi-abelian setting by proving a comparison theorem for simplicial resolutions. This leads to the result that any two projective simplicial resolutions, the definition of which requires slightly more care in the semi-abelian setting, give rise to the same homology. Thus again the homology theory only depends on the projective class. The second viewpoint uses Hopf formulae to define homology, and works in a non-monadic setting; it only requires a semi-abelian category with enough projectives. Even this slightly weaker setting leads to strong results such as a long exact homology sequence, the Everaert sequence, which is a generalised and extended version of the Stallings-Stammbach sequence known for groups. Hopf formulae use projective presentations of objects, and this is closer to the abelian philosophy of using any projective resolution, rather than a special functorial one generated by a comonad. To define higher Hopf formulae for the higher homology objects the use of categorical Galois theory is crucial. This theory allows a choice of Birkhoff subcategory to generate a class of central extensions, which play a big role not only in the definition via Hopf formulae but also in our third viewpoint. This final and new viewpoint we consider is homology via satellites or pointwise Kan extensions. This makes the universal properties of the homology objects apparent, giving a useful new tool in dealing with statements about homology. The driving motivation behind this point of view is the Everaert sequence mentioned above. Janelidze's theory of generalised satellites enables us to use the universal properties of the Everaert sequence to interpret homology as a pointwise Kan extension, or limit. In the first instance, this allows us to calculate homology step by step, and it removes the need for projective objects from the definition. Furthermore, we show that homology is the limit of the diagram consisting of the kernels of all central extensions of a given object, which forges a strong connection between homology and cohomology. When enough projectives are available, we can interpret homology as calculating fixed points of endomorphisms of a given projective presentation

The fundamental group functor as a Kan extension

We prove that the fundamental group functor from categorical Galois theory may be computed as a Kan extension.Comment: Final published version. 26 pages. Dedicated to Rene Guitart on the occasion of his sixty-fifth birthda

Books

LOCALISATION OF BRAIN LESIONS AND DEVELOPMENTAL FUNCTIONS*Mariani Foundation Paediatric Neurology: 9. Edited by D Riva and A Benton. Pp. vi + 165. Illustrated. £39. John Libbey & Co Ltd. 2000. ISBN 0-86196-599x.SPORTS ENDOCRINOLOGY Contemporary Endocrinology. Edited by Michelle P Warren and Naama W Constantini. Pp. x + 486. US$ 135. The Humana Press. 2000. ISBN 0-89603-586-7.SPORTS MEDICINE HANDBOOK* Edited by Roger Hackney and Angus Wallace. Pp. x + 495. Illustrated. £75. 1999. BMJ. ISBN 0-7279-1031-0

On satellites in semi-abelian categories: Homology without projectives

Working in a semi-abelian context, we use Janelidze's theory of generalised satellites to study universal properties of the Everaert long exact homology sequence. This results in a new definition of homology which does not depend on the existence of projective objects. We explore the relations with other notions of homology, and thus prove a version of the higher Hopf formulae. We also work out some examples.Comment: 29 pages; major changes in Example 4.15, minor changes throughout the tex

Ethnic differences in regional adipose tissue oestrogen receptor gene expression

Studies have shown ethnic differences in body fat distribution, characterised by greater peripheral and less central fat accumulation in black compared to white South African (SA) women. As sex hormones play an important role in body fat distribution, our study aimed to determine whether differences in body fat distribution between black and white SA women were associated with subcutaneous adipose tissue (SAT) expression of oestrogen receptors (ERA and ERB) and aromatase (CYP19A1). Body fat distribution (DXA and CT) and ERA, ERB and CYP19A1 expression in abdominal and gluteal SAT were measured in 26 black and 22 white SA women. Abdominal SAT ERA and ERB did not differ by ethnicity or BMI. Gluteal ERA was higher (1.08 ± 0.06 vs 0.99 ± 0.05, P < 0.001) and ERB was lower (0.99 ± 0.06 vs 1.10 ± 0.07, P < 0.001) in black vs white SA women. CYP19A1 increased with obesity in all depots (P < 0.001). In both black and white SA women, gluteal ERA was associated with lower central fat mass (FM) and greater gynoid FM (P < 0.05), while the inverse association was shown for CYP19A1 in all depots (P < 0.01). In conclusion, ethnic differences in gluteal ERA expression were associated with differences in body fat distribution previously reported between black and white SA women

Fasting substrate oxidation in relation to habitual dietary fat intake and insulin resistance in non-diabetic women: a case for metabolic flexibility?

BACKGROUND: Metabolic flexibility described as "the capacity of the body to match fuel oxidation to fuel availability" has been implicated in insulin resistance. We examined fasting substrate oxidation in relation to dietary macronutrient intake, and markers of insulin resistance in otherwise healthy women, with and without a family history of diabetes mellitus (FH DM). METHODS: We measured body composition (dual x-ray absorptiometry), visceral and subcutaneous adipose tissue area (VAT, SAT, using Computerised Tomography), fasting [glucose], [insulin], [free fatty acids], [blood lipids], insulin resistance (HOMA-IR), resting energy expenditure (REE), respiratory exchange ratio(RER) and self-reported physical activity in a convenience sample of 180 women (18-45 yrs). A food frequency questionnaire was used to assess energy intake (EI) and calculate the RER: Food Quotient (FQ) ratio. Only those with EI:REE (1.05 -2.28) were included (N=140). Insulin resistance was defined HOMA-IR (>1.95). RESULTS: The Insulin Resistant (IR) group had higher energy, carbohydrate and protein intakes (p<0.05) and lower PA levels than Insulin Sensitive (IS) group (P<0.001), but there were no differences in RER or RER:FQ between groups. However, nearly 50% of the variance in HOMA-IR was explained by age, body fat %, VAT, RER:FQ and FH DM (adjusted R2=0.50, p<0.0001). Insulin-resistant women, and those with FH DM had a higher RER:FQ than their counterparts (p<0.01), independent of body fat % or distribution. CONCLUSION: In these apparently healthy, weight-stable women, insulin resistance and FH DM were associated with lower fat oxidation in relation to dietary fat intake, suggesting lower metabolic flexibility

Association between ethnicity and obesity with high-density lipoprotein (HDL) function and subclass distribution

Abstract Background Obesity and low high-density lipoprotein-cholesterol (HDL-C) levels are associated with cardiovascular risk. Surprisingly, despite a greater prevalence of obesity and lower HDL concentrations than white women, black South African women are relatively protected against ischaemic heart disease. Methods We investigated whether this apparent discrepancy may be related to different HDL function and subclass distribution in black and white, normal-weight and obese South African women (n = 40). HDL functionality was assessed by measuring paraoxonase (PON) activity, platelet activating factor acetylhydrolase (PAF-AH) activity, Oxygen Radical Absorbance Capacity (ORAC) and quantification of the expression of vascular cell adhesion molecule in endothelial cells. PON-1 and PAF-AH expression was determined in isolated HDL and serum using Western blotting. Levels of large, intermediate and small HDL subclasses were measured using the Lipoprint® system. Results PON activity was lower in white compared to black women (0.49 ± 0.09 U/L vs 0.78 ± 0.10 U/L, p < 0.05), regardless of PON-1 protein levels. Obese black women had lower PAF-AH activity (9.34 ± 1.15 U/L vs 13.89 ± 1.21 U/L, p <0.05) and HDL-associated PAF-AH expression compared to obese white women. Compared to normal-weight women, obese women had lower large HDL, greater intermediate and small HDL; an effect that was more pronounced in white women than black women. There were no differences in antioxidant capacity or anti-inflammatory function across groups. Conclusions Our data show that both obesity and ethnicity are associated with differences in HDL functionality, while obesity was associated with decreases in large HDL subclass distribution. Measuring HDL functionality and subclass may, therefore, be important factors to consider when assessing cardiovascular risk

Estimating the burden of disease attributable to excess body weight in South Africa in 2000

Objective. To estimate the burden of disease attributable to excess body weight using the body mass index (BMI), by age and sex, in South Africa in 2000. Design. World Health Organization comparative risk assessment (CRA) methodology was followed. Re-analysis of the 1998 South Africa Demographic and Health Survey data provided mean BMI estimates by age and sex. Populationattributable fractions were calculated and applied to revised burden of disease estimates. Monte Carlo simulation-modelling techniques were used for the uncertainty analysis. Setting. South Africa. Subjects. Adults 30 years of age. Outcome measures. Deaths and disability-adjusted life years (DALYs) from ischaemic heart disease, ischaemic stroke, hypertensive disease, osteoarthritis, type 2 diabetes mellitus, and selected cancers. Results. Overall, 87% of type 2 diabetes, 68% of hypertensive disease, 61% of endometrial cancer, 45% of ischaemic stroke, 38% of ischaemic heart disease, 31% of kidney cancer, 24% of osteoarthritis, 17% of colon cancer, and 13% of postmenopausal breast cancer were attributable to a BMI 21 kg/m2. Excess body weight is estimated to have caused 36 504 deaths (95% uncertainty interval 31 018 - 38 637) or 7% (95% uncertainty interval 6.0 - 7.4%) of all deaths in 2000, and 462 338 DALYs (95% uncertainty interval 396 512 - 478 847) or 2.9% of all DALYs (95% uncertainty interval 2.4 - 3.0%). The burden in females was approximately double that in males. Conclusions. This study shows the importance of recognising excess body weight as a major risk to health, particularly among females, highlighting the need to develop, implement and evaluate comprehensive interventions to achieve lasting change in the determinants and impact of excess body weight