Internal Cat-1 and XMod

Yıl 2022, Sayı: 38, 79 - 87, 31.03.2022

Elis Soylu Yılmaz Ummahan Ege Arslan

https://doi.org/10.53570/jnt.1080975

Cited By: 3

Öz

In this study, internal categories in the category of cat-1 groups, 1-cat, are determined, and it is investigated whether there is a natural equivalence between the category of these categories and the category of internal categories within the category of crossed modules of groups, XMod.

Anahtar Kelimeler

Crossed module, Cat-1 group, Internal category, Natural equivalence

Kaynakça

• J. L. Loday, Spaces with Finitely Many Nontrivial Homotopy Groups, Journal of Pure and Applied Algebra 24 (1982) 179–202.
• The GAP Group, GAP-Groups, Algorithms and Programming, Version 4.11.1 (https://www.gapsystem. org), (2021).
• T. Porter, Internal Categories and Crossed Modules, In Category Theory, Springer, Berlin, Heidelberg (1982) 249–255.
• T. Porter, Extensions, Crossed Modules and Internal Categories in Categories of Groups with Operations, Proceedings of Edinburgh Mathematical Society, 30 (1987) 373–381.
• M. Forrester-Barker, Group Objects and Internal Categories, arXiv preprint math/0212065, (2002).
• R. Brown, J. P. Higgins, R. Sivera, Nonabelian Algebraic Topology, EMS Tracts in Mathematics 15 (2011) 703 pages.
• T. Porter, Homotopy Quantum Field Theories Meets the Crossed Menagerie: An Introduction to HQFTs and their Relationship with Things Simplicial and with lots of Crossed Gadgetry, Notes prepared for the Workshop and School on Higher Gauge Theory, TQFT and Quantum Gravity Lisbon (2011) 344 pages.
• K. J. Norrie, Actions and Automorphisms of Crossed Modules, Bulletin de la Societe Mathematique de France 118 (1990), 129–146.
• T. Şahan, J. J. Mohammed, Categories Internal to Crossed Modules, Sakarya University Journal of Science 23(4) (2019) 519–531.
• J. J. Mohammed, On the Internal Categories within the Category of Crossed Modules, Master’s Thesis, Aksaray University (2018), Aksaray, Turkey.
• G. Janelidze, Internal Crossed Modules, Georgian Mathematical Journal, 10 (2003) 99-114.