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Internal Cat-1 and XMod

Year 2022, Issue: 38, 79 - 87, 31.03.2022
https://doi.org/10.53570/jnt.1080975

Abstract

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.

References

  • 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.
Year 2022, Issue: 38, 79 - 87, 31.03.2022
https://doi.org/10.53570/jnt.1080975

Abstract

References

  • 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.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Elis Soylu Yılmaz 0000-0002-0869-310X

Ummahan Ege Arslan 0000-0002-2995-0718

Publication Date March 31, 2022
Submission Date March 1, 2022
Published in Issue Year 2022 Issue: 38

Cite

APA Soylu Yılmaz, E., & Ege Arslan, U. (2022). Internal Cat-1 and XMod. Journal of New Theory(38), 79-87. https://doi.org/10.53570/jnt.1080975
AMA Soylu Yılmaz E, Ege Arslan U. Internal Cat-1 and XMod. JNT. March 2022;(38):79-87. doi:10.53570/jnt.1080975
Chicago Soylu Yılmaz, Elis, and Ummahan Ege Arslan. “Internal Cat-1 and XMod”. Journal of New Theory, no. 38 (March 2022): 79-87. https://doi.org/10.53570/jnt.1080975.
EndNote Soylu Yılmaz E, Ege Arslan U (March 1, 2022) Internal Cat-1 and XMod. Journal of New Theory 38 79–87.
IEEE E. Soylu Yılmaz and U. Ege Arslan, “Internal Cat-1 and XMod”, JNT, no. 38, pp. 79–87, March 2022, doi: 10.53570/jnt.1080975.
ISNAD Soylu Yılmaz, Elis - Ege Arslan, Ummahan. “Internal Cat-1 and XMod”. Journal of New Theory 38 (March 2022), 79-87. https://doi.org/10.53570/jnt.1080975.
JAMA Soylu Yılmaz E, Ege Arslan U. Internal Cat-1 and XMod. JNT. 2022;:79–87.
MLA Soylu Yılmaz, Elis and Ummahan Ege Arslan. “Internal Cat-1 and XMod”. Journal of New Theory, no. 38, 2022, pp. 79-87, doi:10.53570/jnt.1080975.
Vancouver Soylu Yılmaz E, Ege Arslan U. Internal Cat-1 and XMod. JNT. 2022(38):79-87.


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