Affiliation:
1. Eskişehir Osmangazi Üniversitesi
Abstract
In this work, we defined a new category called 4-Dimensional 2-crossed modules. We identified the subobjects and ideals in this category. The notion of the subobject is a generalization of ideas like subsets from set theory, subspaces from topology, and subgroups from group theory. We then exemplified subobjects and ideals in the category of 4-Dimensional 2-crossed modules. A quotient object is the dual concept of a subobject. Concepts like quotient sets, spaces, groups, graphs, etc. are generalized with the notion of a quotient object. Using the ideal, we obtain the quotient of two subobjects and prove that the intersection of finite ideals is also an ideal in this category.
Reference15 articles.
1. D. Conduché, Modules Croisés Généralisés de Longueur 2, Journal of Pure and Applied Algebra 34 (2-3) (1984) 155–178.
2. A. R. Grandjeán, M. J. Vale, 2-Modulos Cruzados en la Cohomologia de André-Quillen, Memorias de la Real Academia de Ciencias 22 (1986) 1–28.
3. G. Ellis, Crossed Squares and Combinatorial Homotopy, Mathematische Zeitschrift 214 (1) (1993) 93–110.
4. H. J. Baues, Combinatorial Homotopy and 4-Dimensional Complexes, Berlin, De Gruyter, 2011.
5. R. Brown, N. D. Gilbert, Algebraic Models of 3-Types and Automorphism Structures for Crossed Modules, In Proceedings of the London Mathematical Society 59 (1) (1989) 51–73.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献