Group-2-groupoids and 2G-crossed modules
Yıl: 2019 Cilt: 48 Sayı: 5 Sayfa Aralığı: 1388 - 1397 Metin Dili: İngilizce DOI: 10.15672/HJMS.2018.580 İndeks Tarihi: 04-04-2020
Group-2-groupoids and 2G-crossed modules
Öz: In this paper, we introduce the notion of a group-2-groupoid as a group object in thecategory of 2-groupoids. We also obtain a 2G-crossed module by using the structure ofa group-2-groupoid. Then we prove that the category Gp2Gd of group-2-groupoids andthe category 2GXMod of 2G-crossed modules are equivalent.
Anahtar Kelime: Konular:
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] N. Alemdar and O. Mucuk, The Liftings of R-Modules to Covering Groupoid, Hacet. J. Math. Stat. 41 (6), 813-822, 2012.
- [2] J.C. Baez, An Introduction to n-Categories, in: Moggi E., Rosolini G. (eds) Category Theory and Computer Science, Lecture Notes in Computer Science 1290, Springer, Berlin, Heidelberg, 1997, https://doi.org/10.1007/BFb0026978.
- [3] J.C. Baez, A. Baratin, L. Freidel and D.K. Wise, Infinite-Dimensional Representa- tions of 2-Groups, Mem. Amer. Math. Soc. 219, Number 1032, 2012.
- [4] J.C. Baez and A.D. Lauda, Higher-dimensional Algebra. V. 2-groups, Theory Appl. Categ. 12, 423-491, 2004.
- [5] J.C. Baez and D. Stevenson The Classifying Space of a Topological 2-Group, in: Al- gebraic Topology. Abel Symposia 4, Springer, Berlin, Heidelberg, 2009.
- [6] R. Brown, From Groups to Groupoids: A Brief Survey, Bull. London Math. Soc. 19, 113-134, 1987.
- [7] R. Brown and C.B. Spencer, G-groupoids, Crossed Modules and The Fundamental Groupoid of a Topological Group, Proc. Konn. Ned. Akad. v. Wet. 79, 296-302 1976.
- [8] M. Forrester-Barker, Group objects and internal categories, Preprint arXiv: math/0212065v1, 2002.
- [9] P.J. Higgins, Categories and Groupoids, Van Nostrand, New York, 1971.
- [10] S. Maclane, Categories for the Working Mathematician, Graduate Text in Mathemat- ics, Vol. 5, Springer-Verlag, New York, 1971.
- [11] O. Mucuk, Coverings and ring-groupoids, Geor. Math. J. 5, 475-482, 1998. [12] O. Mucuk, B. Bagriyanik, N. Alemdar and T. Şahan, Group-Groupoids And Mon- odromy Groupoids, Topology Appl. 158 (15), 2034-2042, 2011.
- [13] O. Mucuk, T. Şahan and N. Alemdar, Normality and Quotients in Crossed Modules and Group-groupoids, Appl. Categor. Struct. 23 (3), 415-428, 2015.
- [14] B. Noohi, Notes on 2-Groupoids, 2-Groups and Crossed Modules, Homology Homo- topy Appl. 9 (1), 75-106, 2007.
- [15] T. Porter, Extensions, Crossed Modules and Internal Categories in Categories of Groups With Operations, Proc. Edinb. Math. Soc. 30, 371-381, 1987.
- [16] J.H.C. Whitehead, Note on a previous paper entitled "On adding relations to homo- topy group", Ann. Math. 47, 806-810, 1946.
- [17] J.H.C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc. 55, 453-496, 1949.
APA | Alemdar N, Temel S (2019). Group-2-groupoids and 2G-crossed modules. , 1388 - 1397. 10.15672/HJMS.2018.580 |
Chicago | Alemdar Nazmiye,Temel Sedat Group-2-groupoids and 2G-crossed modules. (2019): 1388 - 1397. 10.15672/HJMS.2018.580 |
MLA | Alemdar Nazmiye,Temel Sedat Group-2-groupoids and 2G-crossed modules. , 2019, ss.1388 - 1397. 10.15672/HJMS.2018.580 |
AMA | Alemdar N,Temel S Group-2-groupoids and 2G-crossed modules. . 2019; 1388 - 1397. 10.15672/HJMS.2018.580 |
Vancouver | Alemdar N,Temel S Group-2-groupoids and 2G-crossed modules. . 2019; 1388 - 1397. 10.15672/HJMS.2018.580 |
IEEE | Alemdar N,Temel S "Group-2-groupoids and 2G-crossed modules." , ss.1388 - 1397, 2019. 10.15672/HJMS.2018.580 |
ISNAD | Alemdar, Nazmiye - Temel, Sedat. "Group-2-groupoids and 2G-crossed modules". (2019), 1388-1397. https://doi.org/10.15672/HJMS.2018.580 |
APA | Alemdar N, Temel S (2019). Group-2-groupoids and 2G-crossed modules. Hacettepe Journal of Mathematics and Statistics, 48(5), 1388 - 1397. 10.15672/HJMS.2018.580 |
Chicago | Alemdar Nazmiye,Temel Sedat Group-2-groupoids and 2G-crossed modules. Hacettepe Journal of Mathematics and Statistics 48, no.5 (2019): 1388 - 1397. 10.15672/HJMS.2018.580 |
MLA | Alemdar Nazmiye,Temel Sedat Group-2-groupoids and 2G-crossed modules. Hacettepe Journal of Mathematics and Statistics, vol.48, no.5, 2019, ss.1388 - 1397. 10.15672/HJMS.2018.580 |
AMA | Alemdar N,Temel S Group-2-groupoids and 2G-crossed modules. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1388 - 1397. 10.15672/HJMS.2018.580 |
Vancouver | Alemdar N,Temel S Group-2-groupoids and 2G-crossed modules. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1388 - 1397. 10.15672/HJMS.2018.580 |
IEEE | Alemdar N,Temel S "Group-2-groupoids and 2G-crossed modules." Hacettepe Journal of Mathematics and Statistics, 48, ss.1388 - 1397, 2019. 10.15672/HJMS.2018.580 |
ISNAD | Alemdar, Nazmiye - Temel, Sedat. "Group-2-groupoids and 2G-crossed modules". Hacettepe Journal of Mathematics and Statistics 48/5 (2019), 1388-1397. https://doi.org/10.15672/HJMS.2018.580 |