ON INTERNAL CATEGORIES IN HIGHER DIMENSIONAL GROUPS

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. [1] M. Alp, Left adjoint of pullback cat1-groups, Turkish journal of Mathematics, Vol. 23, N. 2, 243-249 (1999).
2. [2] J.-L. Loday, Spaces with finitely many nontrivial homotopy groups, Journal of Pure and Applied Algebra , Vol. 24, 179-202 (1982).
3. [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. [4] J. J. Mohammed, On the internal categories within the category of crossed modules, M.Sc. Thesis, Aksaray University, (2018).
5. [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. [6] E. Soylu Yılmaz and U. Ege Arslan, Internal Cat-1 and XMod, Journal of New Theory, Vol. 38, 79-87 (2022).
7. [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. [8] J.H.C. Whitehead, Combinatorial Homotopy II, Bulletin American Mathematical Society, 55, 453-496 (1949).