Isoclinism and Stem Structures of 2-Groups

Tunçar Şahan; Onur Soyyiğit

doi:10.53570/jnt.1726569

Isoclinism and Stem Structures of 2-Groups

Abstract

This study investigates the concept of isoclinism in the category of 2-groups by extending classical group-theoretic notions to higher categorical structures. Building on the categorical equivalence between crossed modules and 2-groups, the paper characterizes isoclinism for 2-groups through commutator maps and explores its key properties. Notably, it demonstrates that isoclinism forms an equivalence relation in the category of 2-groups, similar to the group and crossed module contexts. The paper further proves that every 2-group is isoclinic to a stem 2-group and establishes that isoclinism between 2-groups implies the corresponding isoclinism between their associated crossed modules. These results contribute to the broader understanding of homotopy-theoretic and categorical classifications within algebraic topology and category theory.

Keywords

References

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Details

Primary Language

English

Subjects

Category Theory, K Theory, Homological Algebra

Journal Section

Research Article

Authors

Tunçar Şahan ^*
0000-0002-6552-4695
Türkiye

Onur Soyyiğit
0000-0002-6536-5292
Türkiye

Early Pub Date

September 30, 2025

Publication Date

September 30, 2025

Submission Date

June 24, 2025

Acceptance Date

August 25, 2025

Published in Issue

Year 2025 Number: 52

DOI

https://doi.org/10.53570/jnt.1726569

IZ

https://izlik.org/JA27LP27PA

Cite

RIS / Bibtex

APA

Şahan, T., & Soyyiğit, O. (2025). Isoclinism and Stem Structures of 2-Groups. Journal of New Theory, 52, 9-26. https://doi.org/10.53570/jnt.1726569

AMA

1.Şahan T, Soyyiğit O. Isoclinism and Stem Structures of 2-Groups. JNT. 2025;(52):9-26. doi:10.53570/jnt.1726569

Chicago

Şahan, Tunçar, and Onur Soyyiğit. 2025. “Isoclinism and Stem Structures of 2-Groups”. Journal of New Theory, nos. 52: 9-26. https://doi.org/10.53570/jnt.1726569.

EndNote

Şahan T, Soyyiğit O (September 1, 2025) Isoclinism and Stem Structures of 2-Groups. Journal of New Theory 52 9–26.

IEEE

[1]T. Şahan and O. Soyyiğit, “Isoclinism and Stem Structures of 2-Groups”, JNT, no. 52, pp. 9–26, Sept. 2025, doi: 10.53570/jnt.1726569.

ISNAD

Şahan, Tunçar - Soyyiğit, Onur. “Isoclinism and Stem Structures of 2-Groups”. Journal of New Theory. 52 (September 1, 2025): 9-26. https://doi.org/10.53570/jnt.1726569.

JAMA

1.Şahan T, Soyyiğit O. Isoclinism and Stem Structures of 2-Groups. JNT. 2025;:9–26.

MLA

Şahan, Tunçar, and Onur Soyyiğit. “Isoclinism and Stem Structures of 2-Groups”. Journal of New Theory, no. 52, Sept. 2025, pp. 9-26, doi:10.53570/jnt.1726569.

Vancouver

1.Tunçar Şahan, Onur Soyyiğit. Isoclinism and Stem Structures of 2-Groups. JNT. 2025 Sep. 1;(52):9-26. doi:10.53570/jnt.1726569