Grothendieck categories as a bilocalization of linear sites

We prove that the 2-category Grt of Grothendieck abelian categories with colimit preserving functors and natural transformations is a bicategory of fractions in the sense of Pronk of the 2-category Site of linear sites with continuous morphisms of sites and natural transformations. This result can potentially be used to make the tensor product of Grothendieck categories from earlier work by Lowen, Shoikhet and the author into a bi-monoidal structure on Grt

Gabriel-Ulmer duality for topoi and its relation with site presentations

Let $\kappa$ be a regular cardinal. We study Gabriel-Ulmer duality when one restricts the 2-category of locally $\kappa$-presentable categories with $\kappa$-accessible right adjoints to its locally full sub-2-category of $\kappa$-presentable Grothendieck topoi with geometric $\kappa$-accessible morphisms. In particular, we provide a full understanding of the locally full sub-2-category of the 2-category of $\kappa$-small cocomplete categories with $\kappa$-colimit preserving functors arising as the corresponding 2-category of presentations via the restriction. We analyse the relation of these presentations of Grothendieck topoi with site presentations and we show that the 2-category of locally $\kappa$-presentable Grothendieck topoi with geometric $\kappa$-accessible morphisms is a reflective sub-bicategory of the full sub-2-category of the 2-category of sites with morphisms of sites genearated by the weakly $\kappa$-ary sites in the sense of Shulman [37].Comment: 25 page

On the tensor product of linear sites and Grothendieck categories

We define a tensor product of linear sites, and a resulting tensor product of Grothendieck categories based upon their representations as categories of linear sheaves. We show that our tensor product is a special case of the tensor product of locally presentable linear categories, and that the tensor product of locally coherent Grothendieck categories is locally coherent if and only if the Deligne tensor product of their abelian categories of finitely presented objects exists. We describe the tensor product of non-commutative projective schemes in terms of Z-algebras, and show that for projective schemes our tensor product corresponds to the usual product scheme.Comment: New sections 5.3 on the alpha-Deligne tensor product and 5.4 on future prospect

Exponentiable Grothendieck categories in flat Algebraic Geometry

We introduce and describe the $2$-category $\mathsf{Grt}_{\flat}$ of Grothendieck categories and flat morphisms between them. First, we show that the tensor product of locally presentable linear categories $\boxtimes$ restricts nicely to $\mathsf{Grt}_{\flat}$. Then, we characterize exponentiable objects with respect to $\boxtimes$: these are continuous Grothendieck categories. In particular, locally finitely presentable Grothendieck categories are exponentiable. Consequently, we have that, for a quasi-compact quasi-separated scheme $X$, the category of quasi-coherent sheaves $\mathsf{Qcoh}(X)$ is exponentiable. Finally, we provide a family of examples and concrete computations of exponentials.Comment: Minor revision. The proofs of Sec 5 have been expanded to make the paper self containe

On the tensor product of well generated dg categories

We endow the homotopy category of well generated (pretriangulated) dg categories with a tensor product satisfying a universal property. The resulting monoidal structure is symmetric and closed with respect to the cocontinuous RHom of dg categories (in the sense of To\"en [26]). We give a construction of the tensor product in terms of localisations of dg derived categories, making use of the enhanced derived Gabriel-Popescu theorem [21]. Given a regular cardinal alpha, we define and construct a tensor product of homotopically alpha-cocomplete dg categories and prove that the well generated tensor product of alpha-continuous derived dg categories (in the sense of [21]) is the alpha-continuous dg derived category of the homotopically alpha-cocomplete tensor product. In particular, this shows that the tensor product of well generated dg categories preserves alpha-compactness

Cytotoxic Activity of Essential Oils of Some Species from Lamiaceae Family

Cancer is considered one of the most lethal diseases in the world, with a prevalence of 439.2 cases and 163.5 deaths per 100,000 inhabitants, in the period from 2011 to 2015; this disease has a greater impact in underdeveloped countries. For the treatment of this disease, a combination of chemotherapy with surgery or radiation is generally used, however, it is not exempt from adverse effects or resistance of the tumor to this type of treatment, for this reason the search for new treatments is constant. The plants are a possible source to achieve this; Lamiaceae is a family of plants widely distributed on the planet and has been used traditionally for the treatment of different diseases, and various essential oils with the potential for cancer treatment have been isolated from this species. The scope of this review is to present 46 essential oils isolated from different species of Lamiaceae which have been tested against different cancer cell lines

Diagnostic Accuracy Study Comparing Hysterosalpingo-Foam Sonography and Hysterosalpingography for Fallopian Tube Patency Assessment

Introduction: Simplified ultrasound-based infertility protocols that appear to provide enough information to plan effective management have been described. Thus, the objective of this study is to compare the diagnostic accuracy of the hysterosalpingo-foam sonography (HyFoSy) in tubal patency testing with the traditional hysterosalpngography (HSG) for establishing a new diagnostic strategy in infertility. Material and Methods: Prospective observational diagnostic accuracy was performed in a private fertility clinic in which 106 women undergoing a preconceptionally visit were recruited. All of them had low risk for tubal disease, had performed an HSG and were negative for Chlamydia trachomatis antibody. Main outcome measures were tubal patency and pain grade. Results: Evaluation of tubal patency by HyFoSy showed a total concordance with the results of the previous HSG in 72.6% (n = 77), and a total discordance for 4.7% (n = 6), with the inter-test agreement Kappa equal to 0.57, which means moderate concordance. Among the patients, 59.1% did not report pain during the procedure, while the remaining 48.1% indicated pain in different degrees; patients usually report less pain and only 6.6% described more pain with HyFoSy than with HSG (OR 6.57 (CI 95% 3.11–13.89)). Clinical outcomes after performing HyFoSy were not affected. Conclusions: HyFoSy is in concordance with HSG regarding tubal patency results and it is a less painful technique than HSG. HyFoSy is more economical and can be performed in an exam room only equipped with an ultrasound scanner. Based on these results, HyFoSy could be the first-choice diagnostic option to assess tubal patency in patients with low risk of tubal disea

N- and S-doped carbons derived from polyacrylonitrile for gases separation

The CO2 capture using adsorption can reduce the carbon footprint, increasing the sustainability of the process without the production of wastes present in commonly used industrial operations. The present research work analyses the effect of the doping-agents incorporation in carbon materials upon adsorption and separation of gases, specifically for carbon dioxide and nitrogen. The carbons precursor was polyacrylonitrile (PAN), which enabled the incorporation of nitrogen atoms in the structure, whereas sulphur doping was reached using pure sulphur after the carbonisation step. The influence of several variables (such as temperature or pressure) and characteristics of synthesised materials (mainly corresponding to surface characteristics) on carbon dioxide separation has been evaluated. Adsorption isotherms were determined for each gas (CO2 and N2) at different temperatures and pressures. Different adsorption models were evaluated to fit the experimental data. In general, the Toth isotherm described better the adsorption for both gases. Important parameters such as CO2/N2 selectivity and heat of adsorption were determined using the IAS theory and the experimental isotherms at different temperatures, respectively. Non-activated carbons generated from PAN carbonisation without sulphur addition showed the highest values of selectivity (up to 400) and adsorption heat (up to 40 kJ mol−1), mainly at low pressures and at low carbon dioxide uptakes, respectively. Furthermore, thanks to their high adsorption capacity, these carbons can be applied for carbon dioxide separation from mixtures with nitrogen