TY - JOUR T1 - LIMITS IN THE CATEGORY OF 2-GENERALIZED CROSSED MODULES TT - LIMITS IN THE CATEGORY OF 2-GENERALIZED CROSSED MODULES AU - Gülsün Akay, Hatice PY - 2025 DA - August Y2 - 2025 DO - 10.20290/estubtdb.1606064 JF - Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler JO - Estuscience - Theory PB - Eskişehir Teknik Üniversitesi WT - DergiPark SN - 2667-419X SP - 92 EP - 103 VL - 13 IS - 2 LA - en AB - In a previous study, limits were calculated within the category of 2-crossed modules of groups over a fixed group R, where the group actions involved were specifically taken to be conjugation actions. While this framework provides a rich algebraic structure for constructing certain homotopical and categorical structures, the limitation of conjugation-based actions restricts the flexibility of this approach. In this paper, we extend this framework by introducing the notion of 2-generalized crossed modules (2GCM), which generalize the structure of 2-crossed modules by allowing more flexible and arbitrary group actions, rather than restricting them to conjugation actions. Furthermore, we prove that the category of 2-generalized crossed modules is finitely complete, meaning that it possesses all finite limits, such as products and equalizers. This property is important for higher-level categorical analysis and supports the application of 2-generalized crossed modules in both theoretical and applied contexts, particularly in higher-dimensional algebra and homotopy theory. KW - 2-Generalized crossed module KW - Limit KW - Product N2 - In a previous study, limits were calculated within the category of 2-crossed modules of groups over a fixed group R, where the group actions involved were specifically taken to be conjugation actions. While this framework provides a rich algebraic structure for constructing certain homotopical and categorical structures, the limitation of conjugation-based actions restricts the flexibility of this approach. In this paper, we extend this framework by introducing the notion of 2-generalized crossed modules (2GCM), which generalize the structure of 2-crossed modules by allowing more flexible and arbitrary group actions, rather than restricting them to conjugation actions. Furthermore, we prove that the category of 2-generalized crossed modules is finitely complete, meaning that it possesses all finite limits, such as products and equalizers. This property is important for higher-level categorical analysis and supports the application of 2-generalized crossed modules in both theoretical and applied contexts, particularly in higher-dimensional algebra and homotopy theory. CR - [1] Yavari M, Salemkar A. The category of generalized crossed modules. 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CR - [16] Yılmaz ES. (Co) Limit calculations in the category of 2-crossed R-modules. Turkish Journal of Mathematics 2022; 46; 2902-2915. CR - [17] Ege Arslan U, Akça İİ, Onarlı G, Avcıoğlu O. Fibrations of 2-crossed modules. Math Meth Appl Sci 2019; 42: 5293–5304. UR - https://doi.org/10.20290/estubtdb.1606064 L1 - https://dergipark.org.tr/tr/download/article-file/4461498 ER -