Category of intervals

Proposition 10.17. For an arbitrary acyclic category C, the category of intervals I(C) is acyclic as well. 

As it turns out, the topology of the category of intervals of an acyclic category is the same as that of the original category itself. 

The interested reader is invited to see how the statement of Theorem 10.19 works out for the categories of intervals depicted in Figure 10.12. 

HRV assesses the modulation of autonomic tone on the sinus node, or simply put, the irregularity of sinus rhythm. Methods of measuring HRV fall under broad categories of being either time domain or frequency domain analyses. Time domain measurements involve statistical analyses of the variability in the R-R interval, while frequency domain measurements use spectral analysis of a series of R-R intervals to classify HRV into ultra-low frequency, very low frequency, low frequency, high frequency, and total power. One method is not better than another as there is no gold standard (65). 

Fig. 1. Hazard ratios, with 95% confidence intervals as floating absolute risks, as estimate of association between category of update mean HbAlc concentration and any end point or deaths related to diabetes and all cause mortality. Reference category (hazard ratio 1.0) is HbAlc <6% with log-linear scales, p-value reflects contribution of glycaemia to multivariate model. Data adjusted for age at diagnosis of diabetes, sex, ethnic group, smoking, presence of albuminuria, systolic blood pressure, high- and low-density lipoprotein cholesterol and triglycerides [2].

In Section 3 we apply this localization theorem to define a model category structure on the category of simplicial sheaves on a site with interval (see [31, 2.2]). We show that this model category structure is always proper (in the sense of [2, Definition 1.2]) and give examples of how some known homotopy categories can be obtained using this construction. 

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