Grothendieck categories and their tensor product as filtered colimits

We present two ways of recovering a Grothendieck category as a filtered colimit of small categories by means of the construction of the (2-)filtered (bi)colimit of categories from [9]. The first one, making use of the fact that Grothendieck categories are locally presentable, allows to recover a Grothendieck category as a filtered colimit of its subcategories of alpha-presentable objects, for alpha varying in the family of small regular cardinals. The second one, making use of the fact that Grothendieck categories are precisely the linear topoi, permits to recover a Grothendieck category as a filtered colimit of its linear site presentations. We then show that the tensor product of Grothendieck categories from [18] can be recovered as a filtered colimit of Kelly's alpha-cocomplete tensor product of the categories of alpha-presentable objects with alpha varying in the family of small regular cardinals. We use this construction to translate the functoriality, associativity and simmetry of Kelly's tensor product to the tensor product of Grothendieck categories

Spectropolarimetric analysis of an active region filament. I. Magnetic and dynamical properties from single component inversions

The determination of the magnetic filed vector in solar filaments is possible by interpreting the Hanle and Zeeman effects in suitable chromospheric spectral lines like those of the He I multiplet at 10830 A. We study the vector magnetic field of an active region filament (NOAA 12087). Spectropolarimetric data of this active region was acquired with the GRIS instrument at the GREGOR telescope and studied simultaneously in the chromosphere with the He I 10830 A multiplet and in the photosphere with the Si I 10827 A line. As it is usual from previous studies, only a single component model is used to infer the magnetic properties of the filament. The results are put into a solar context with the help of the Solar Dynamic Observatory images. Some results clearly point out that a more complex inversion had to be done. Firstly, the Stokes $V$ map of He I does not show any clear signature of the presence of the filament. Secondly, the local azimuth map follows the same pattern than Stokes $V$ as if the polarity of Stokes $V$ were conditioning the inference to very different magnetic field even with similar linear polarization signals. This indication suggests that the Stokes $V$ could be dominated by the below magnetic field coming from the active region, and not, from the filament itself. Those and more evidences will be analyzed in depth and a more complex inversion will be attempted in the second part of this series.Comment: 18 pages, 19 figures, accepted for publication in A&

Polarization of the changing-look quasar J1011+5442

If the disappearance of the broad emission lines observed in changing-look quasars were caused by the obscuration of the quasar core through moving dust clouds in the torus, high linear polarization typical of type 2 quasars would be expected. We measured the polarization of the changing-look quasar J1011+5442 in which the broad emission lines have disappeared between 2003 and 2015. We found a polarization degree compatible with null polarization. This measurement suggests that the observed change of look is not due to a change of obscuration hiding the continuum source and the broad line region, and that the quasar is seen close to the system axis. Our results thus support the idea that the vanishing of the broad emission lines in J1011+5442 is due to an intrinsic dimming of the ionizing continuum source that is most likely caused by a rapid decrease in the rate of accretion onto the supermassive black hole.Comment: Accepted for publication in Astronomy and Astrophysics Letter

A search for magnetic fields on central stars in planetary nebulae

One of the possible mechanisms responsible for the panoply of shapes in planetary nebulae is the presence of magnetic fields that drive the ejection of ionized material during the proto-planetary nebula phase. Therefore, detecting magnetic fields in such objects is of key importance for understanding their dynamics. Still, magnetic fields have not been detected using polarimetry in the central stars of planetary nebulae. Circularly polarized light spectra have been obtained with the Focal Reducer and Low Dispersion Spectrograph at the Very Large Telescope of the European Southern Observatory and the Intermediate dispersion Spectrograph and Imaging System at the William Herschel Telescope. Nineteen planetary nebulae spanning very different morphology and evolutionary stages have been selected. Most of central stars have been observed at different rotation phases to point out evidence of magnetic variability. In this paper, we present the result of two observational campaigns aimed to detect and measure the magnetic field in the central stars of planetary nebulae on the basis of low resolution spectropolarimetry. In the limit of the adopted method, we can state that large scale fields of kG order are not hosted on the central star of planetary nebulae.Comment: Paper accepted to be published in Astronomy and Astrophysics on 20/01/201

Hierarchical analysis of the quiet Sun magnetism

Standard statistical analysis of the magnetic properties of the quiet Sun rely on simple histograms of quantities inferred from maximum-likelihood estimations. Because of the inherent degeneracies, either intrinsic or induced by the noise, this approach is not optimal and can lead to highly biased results. We carry out a meta-analysis of the magnetism of the quiet Sun from Hinode observations using a hierarchical probabilistic method. This model allows us to infer the statistical properties of the magnetic field vector over the observed field-of-view consistently taking into account the uncertainties in each pixel due to noise and degeneracies. Our results point out that the magnetic fields are very weak, below 275 G with 95% credibility, with a slight preference for horizontal fields, although the distribution is not far from a quasi-isotropic distribution.Comment: 9 pages, 4 figures, accepted for publication in A&

Emotion, Psychological Well-Being and Their Influence on Resilience. A Study with Semi-Professional Athletes

The objective of the present study is to analyze the influence of coaches on emotional intelligence and on levels of anxiety, motivation, self-esteem, and resilience among athletes. Five-hundred forty-seven semi-professional athletes between the ages of 16 and 19 participated in this study. Various statistical analyses were conducted which explain the causal relationships between the variables. The results, obtained using a structural equations model, find that while autonomy support positively predicts emotional intelligence, perceived control predicts it negatively. Moreover, emotional intelligence positively predicts self-esteem and self-determined motivation, but negatively predicts anxiety. Other results show that self-esteem positively predicts self-determined motivation, whereas anxiety predicts it negatively. Finally, self-determined motivation positively predicts resilience. Indeed, the study demonstrates the influence and the importance of coaches in relation to the emotional intelligence, psychological well-being, and motivational processes of adolescent athletes when the latter engage in their respective sports. These results help to better understand how different behavioral, emotional, and social aspects belonging to the athlete interrelate with one another during competition