ON INTERNAL CATEGORIES IN HIGHER DIMENSIONAL GROUPS

Year 2022, Volume: 5 Issue: 2, 129 - 138, 31.07.2022

Ummahan Ege Arslan , Elis Soylu Yılmaz

https://doi.org/10.33773/jum.1115099

Cited By: 1

https://izlik.org/JA43CY96SF

Abstract

In this paper, we demonstrated the equivalencies of internal categories
of cat-1 groups and cat-2 groups structures using some related equivalent
categories.

Keywords

Cat1-group , Internal category , Crossed Module

References

• [1] M. Alp, Left adjoint of pullback cat1-groups, Turkish journal of Mathematics, Vol. 23, N. 2, 243-249 (1999).
• [2] J.-L. Loday, Spaces with finitely many nontrivial homotopy groups, Journal of Pure and Applied Algebra , Vol. 24, 179-202 (1982).
• [3] T. Sahan and J. J. Mohammed, Categories Internal to Crossed Modules, Sakarya University Journal of Science, Vol. 23, N. 4, 519-531 (2019).
• [4] J. J. Mohammed, On the internal categories within the category of crossed modules, M.Sc. Thesis, Aksaray University, (2018).
• [5] 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, Lecture Notes (2011).
• [6] E. Soylu Yılmaz and U. Ege Arslan, Internal Cat-1 and XMod, Journal of New Theory, Vol. 38, 79-87 (2022).
• [7] D. Guin-Walery and J.-L. Loday, Obstructions `a l’excision en K-th´eorie alg`ebrique, in Evanston Conference on Algebraic K-theory, Lecture Notes in Maths., Springer, Vol. 854, 179 – 216 (1981).
• [8] J.H.C. Whitehead, Combinatorial Homotopy II, Bulletin American Mathematical Society, 55, 453-496 (1949).