In this paper‎, ‎we give the notions of crossed polymodule and cat$^1$-polygroup‎ ‎as a generalization of Loday's definition‎. ‎Then‎, ‎we define the pullback cat$^1$-polygroup and we obtain some results in this respect‎. ‎Specially‎, ‎we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group‎.

in this paper‎, ‎we give the notions of crossed polymodule and cat$^1$-polygroup‎ ‎as a generalization of loday's definition‎. ‎then‎, ‎we define the pullback cat$^1$-polygroup and we obtain some results in this respect‎. ‎specially‎, ‎we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group‎.

A simplicial group is a object in the category of groups. very nice application which polygroup given this paper. Using polygroups instead groups, we already had good results from well known properties due to Loday. Loday proved that crossed module, cat1-group, categories and whose Moore complex length one are equivalent. Loday’s idea present functor groups polygroups. We show there exist cat1-...

This paper concerns a relationship between soft sets and n-ary polygroups. We consider the notion of an n-ary polygroup as a generalization of a polygroup and apply the notion of soft sets to n-ary polygroups. Some related notions are defined and several basic properties are discussed by using the soft set theory. Furthermore, we propose the homomorphism of n-ary polygroups and investigate the ...

Calcium-related proteins include the calcium transporters 1 and 2 (CaT1 and CaT2), plasma membrane Ca2+-ATPase 1b (PMCA1b), and calbindin-D9k and -D28k. The expression of CaT1 and PMCA1b and their potential roles in the uterine tissue remain to be clarified. Thus, in the present study, the expression patterns of CaT1 and PMCA1b were examined to predict their roles in rat uterus during the estro...

In the present study, we sought to elucidate the contribution of the Cryptococcus neoformans catalase gene family to antioxidant defense. We employed bioinformatics techniques to identify four members of the C. neoformans catalase gene family and created mutants lacking single or multiple catalase genes. Based on a phylogenetic analysis, CAT1 and CAT3 encode putative spore-specific catalases, C...

We examined the expression of calcium transporter 1 (CaT1) and epithelial calcium channel (ECaC) mRNA in the duodenum and kidney of mice. Intestinal CaT1 mRNA level increased 30-fold at weaning, coincident with the induction of calbindin-D(9k) expression. In contrast, renal CaT1 and ECaC mRNA expression was equal until weaning when ECaC mRNA is induced and CaT1 mRNA levels fall 70%. Long- and s...

‎We firstly prove the completeness of the category of crossed modules in a modified category of interest‎. ‎Afterwards‎, ‎we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows‎. ‎These constructions unify many corresponding results for the cases of groups‎, ‎commutative algebras and can also be adapted to ...

The calcium release-activated calcium channel (CRAC) is a highly Ca(2+)-selective ion channel that is activated on depletion of inositol triphosphate (IP(3))-sensitive intracellular Ca(2+) stores. It was recently reported that CaT1, a member of the TRP family of cation channels, exhibits the unique biophysical properties of CRAC, which led to the conclusion that CaT1 comprises all or part of th...