Year 2019, Volume 48 , Issue 5, Pages 1388 - 1397 2019-10-08

Group-2-groupoids and 2G-crossed modules

Nazmiye Alemdar [1] , Sedat Temel [2]


In this paper, we introduce the notion of a group-2-groupoid as a group object in the category of 2-groupoids. We also obtain a 2G-crossed module by using the structure of a group-2-groupoid. Then we prove that the  category Gp2Gd of group-2-groupoids and the category 2GXMod of 2G-crossed modules are equivalent.
group-2-groupoid, 2G-crossed module
  • [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.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-0819-6613
Author: Nazmiye Alemdar (Primary Author)

Orcid: 0000-0001-6553-8758
Author: Sedat Temel

Dates

Publication Date : October 8, 2019

Bibtex @research article { hujms629837, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1388 - 1397}, doi = {}, title = {Group-2-groupoids and 2G-crossed modules}, key = {cite}, author = {Alemdar, Nazmiye and Temel, Sedat} }
APA Alemdar, N , Temel, S . (2019). Group-2-groupoids and 2G-crossed modules. Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1388-1397 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/49321/629837
MLA Alemdar, N , Temel, S . "Group-2-groupoids and 2G-crossed modules". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1388-1397 <https://dergipark.org.tr/en/pub/hujms/issue/49321/629837>
Chicago Alemdar, N , Temel, S . "Group-2-groupoids and 2G-crossed modules". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1388-1397
RIS TY - JOUR T1 - Group-2-groupoids and 2G-crossed modules AU - Nazmiye Alemdar , Sedat Temel Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1388 EP - 1397 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Group-2-groupoids and 2G-crossed modules %A Nazmiye Alemdar , Sedat Temel %T Group-2-groupoids and 2G-crossed modules %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R %U
ISNAD Alemdar, Nazmiye , Temel, Sedat . "Group-2-groupoids and 2G-crossed modules". Hacettepe Journal of Mathematics and Statistics 48 / 5 (October 2019): 1388-1397 .
AMA Alemdar N , Temel S . Group-2-groupoids and 2G-crossed modules. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1388-1397.
Vancouver Alemdar N , Temel S . Group-2-groupoids and 2G-crossed modules. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1397-1388.