Generalized crossed modules and group-groupoids

Abstract

In this present work, we present the concept of a crossed module over generalized groups and we call it a "generalized crossed module". We also define a generalized group-groupoid. Furthermore, we show that the category of generalized crossed modules is equivalent to that of generalized group-groupoids whose object sets are abelian generalized group.

Design, synthesis, characterization and antimicrobial evaluation of some novel hydrazinecarbothioamide, 4‐thiazolidinone and 1,2,4‐triazole‐3‐thione derivatives

“…4-Thiazolidinones have been considered as a pharmacologically active scaffold due to their wide range of reported biological activities in literature. The compounds bearing 4-thiazolidinone moiety have been reported in the literature by their antibacterial, [26] antifungal, [27,28] antitubercular, [29] anticancer, [30][31][32][33] anti-inflammatory, [34] analgesic, [35] anticonvulsant, [36] antiviral, [37,38] cytotoxic [39] and antidiabetic [40] activities. Compounds such as ralitoline (anticonvulsant), pioglitazone (hypoglycemic) and thiazolidomycin (activity against Streptomyces species), based on 4-thiazolidinone pharmacophore are already in clinical use as commercial products ( Figure 2).…”

Generalized groups and module groupoids

“…(cf. [2]) A generalized group groupoid G is a groupoid (νG, G) endowed with the structure of generalized group such that the following maps (1)…”

Normality and quotient in the category of crossed modules within the category of groups with operations

“…In [26] Porter proved a similar result to one in [7] holds for certain algebraic categories, introduced by Orzech [24], which definition was adapted by him and called category of groups with operations. Gürsoy et al [13] generalized the result given in [7] in a different way. They introduced the notion of crossed module over generalized groups which they call it by generalized crossed module and of generalized group-groupoid.…”