On the relative homology of cleft extensions of rings and abelian categories

AbstractWe study the relative homological behaviour of the omnipresent class of cleft extensions of abelian categories. This class of extensions is a natural generalization of the trivial extensions studied in detail by Fossum, Griffith and Reiten and by Palmer and Roos. We apply our results to the relative homology of cleft extensions of rings

C*-Algebras over Topological Spaces: Filtrated K-Theory

We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe a space with four points and two C*-algebras over this space in the bootstrap class that have isomorphic filtrated K-theory but are not KK(X)-equivalent. For this particular space, we enrich filtrated K-theory by another K-theory functor, so that there is again a Universal Coefficient Theorem. Thus the enriched filtrated K-theory is a complete invariant for purely infinite, stable C*-algebras with this particular spectrum and belonging to the appropriate bootstrap class.Comment: Changes to theorem and equation numbering

Both low and high spatial frequencies drive the early posterior negativity in response to snake stimuli

Previous event-related potential (ERP) studies have shown that snake pictures elicit greater early posterior negativity (EPN) compared to other animal pictures. The EPN reflects early selective visual processing of emotionally significant stimuli. Evidence for the role that high and low spatial frequencies play in the early detection of snakes is still inconsistent. The current study aims to clarify this by studying the effect of high and low spatial frequencies on the elevated EPN for snakes separately. Using a rapid serial visual presentation paradigm, participants viewed images of snakes, spiders and birds in three different conditions of filtered spatial frequencies: high spatial frequency, low spatial frequency, and full spatial frequency (the original image). P1 and mean EPN activity in a time window of 225–300 ms after stimulus onset were measured at the occipital cluster (O1, O2, Oz). The results show smaller P1 amplitudes and shorter P1 latencies in response to full-spectrum snake pictures compared to full-spectrum spider and bird pictures, and an increased EPN in response to snake pictures compared to spider and bird pictures in all three filtering conditions. The EPN in response to full-spectrum snake pictures was larger than the EPN in response to filtered snake images. No difference in EPN was found between the snake pictures in the high and low spatial frequency conditions. The results suggest that the roles of high and low spatial frequencies in early automatic attention to snakes are equally important.</p

On exact categories and applications to triangulated adjoints and model structures

We show that Quillen's small object argument works for exact categories under very mild conditions. This has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model structures. In particular, the interplay of different exact structures on the category of complexes of quasi-coherent sheaves leads to a streamlined and generalized version of recent results obtained by Estrada, Gillespie, Guil Asensio, Hovey, J{\o}rgensen, Neeman, Murfet, Prest, Trlifaj and possibly others.Comment: 38 pages; version 2: major revision, more explanation added at several places, reference list updated and extended, misprints correcte

High spatial frequencies drive the early posterior negativity in response to snake pictures

__Introduction__ As snakes were probably the first predators of mammals, they may have been important agents of evolutionary changes in the primate visual system allowing fast visual detection of fearful stimuli (Isbell, 2006). Many EEG studies have established larger early posterior negativity (EPN) in response to snake stimuli when compared to other animal stimuli (e.g., Van Strien et al., 2014). The EPN is an eventrelated potential that reflects early selective visual processing of emotionally significant information. A recent study (Van Strien & Isbell, 2017) has emphasized the importance of the typical scales and scale patterns of the snake skin for the enhanced EPN in response to snake pictures. In the present research, we examined whether the EPN snake effect still exists when these scales are made less visible by blurring snake pictures, that is, we examined the influence of spatial frequency on the EPN snake effect