The group of strong Galois objects associated to a cocommutative Hopf quasigroup

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong) Galois H-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of H-Galois objects introduced by Chase and Sweedler

Smash (co)products and skew pairings

Let [tau] be an invertible skew pairing on (B,H), where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HHYD and there exists a Hopf algebra isomorphism w: B[infinity]H --> B [tau]H in C, where B[infinity]H is a Hopf algebra with (co)algebra structure the smash (co)product and B [tau] H is the Hopf algebra defined by Doi and Takeuchi

Cyano-and ketone-containing selenoesters as multi-target compounds against resistant cancers

Fifteen selenocompounds, comprising of eight ketone-containing selenoesters (K1–K8, also known as oxoselenoesters) and seven cyano-containing selenoesters (N1–N7, known also as cyanoselenoesters), have been designed, synthesized, and evaluated as novel anticancer agents. These compounds are derivatives of previously reported active selenoesters and were prepared following a three-step one-pot synthetic route. The following evaluations were performed in their biological assessment: cytotoxicity determination, selectivity towards cancer cells in respect to non-cancer cells, checkerboard combination assay, ABCB1 inhibition and inhibition of ABCB1 ATPase activity, apoptosis induction, and wound healing assay. As key results, all the compounds showed cytotoxicity against cancer cells at low micromolar concentrations, with cyanoselenoesters being strongly selective. All of the oxoselenoesters, except K4, were potent ABCB1 inhibitors, and two of them, namely K5 and K6, enhanced the activity of doxorubicin in a synergistic manner. The majority of these ketone derivatives modulated the ATPase activity, showed wound healing activity, and induced apoptosis, with K3 being the most potent, with a potency close to that of the reference compound. To summarize, these novel derivatives have promising multi-target activity, and are worthy to be studied more in-depth in future works to gain a greater understanding of their potential applications against cancer.The study was supported by the projects SZTE ÁOK-KKA 2018/270-62-2 of the University of Szeged, Faculty of Medicine and GINOP-2.3.2-15-2016-00038 (Hungary); and Consejo Superior de Investigaciones Científicas (CSIC, Spain, project LINKA20285). This research was funded by VISEGRAD FUND, grant number 22010090; and by the mobility project from the Czech Ministry of Education, Youth and Sports INTER-COST, grant number LTC19007. This article is based upon work from COST Action 17104 , supported by COST (European Cooperation in Science and Technology), (http://www.cost.eu, accessed on 17 September 2021). The study was supported also by two cultural associations: “Trevinca” and “Iniciativas Ropelanas”