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Dergiler / Ikonion Journal of Mathematics / 2023 / Cilt: 5 Sayı: 1

Categorification of Algebras: 2-Algebras

İbrahim AKÇA
Ummahan EGE ARSLAN
Sayfa
1–19
Yayın Tarihi
2023-08-22
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is shown that the category of 2-algebras is equivalent to the category of crossed modules in commutative k-algebras.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper introduces a categorification of k-algebras called 2-algebras, where k is a commutative ring.
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Temel Bulgular & Veri:We define the 2-algebras as a 2-category with single object in which collections of all 1-morphisms and all 2-morphisms are k-algebras.
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Sonuç & Katkı:It is shown that the category of 2-algebras is equivalent to the category of crossed modules in commutative k-algebras.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:2-categories · Crossed modules · Homotopy.

Abstract

This paper introduces a categorification of k-algebras called 2-algebras, where k is a commutative ring. We define the 2-algebras as a 2-category with single object in which collections of all 1-morphisms and all 2-morphisms are k-algebras. It is shown that the category of 2-algebras is equivalent to the category of crossed modules in commutative k-algebras.

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Bu Makaleye Atıf Yap

AKÇA, İ., ARSLAN, U. E. (2023). Categorification of Algebras: 2-Algebras. Ikonion Journal of Mathematics, Cilt: 5 Sayı: 1, 1–19. https://ajindex.com/articles/959501

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Kaynakça (10)

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  2. Baez J.C, Crans A.S. Higher Dimensional Algebra VI: Lie 2-Algebras, Theory and Applications of Categories, 2004; 12: (15), 492-538
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  7. Norrie K.J. Actions and Automorphisms of Crossed Modules, Bull. Soc. Math. France. 1990; 118; 129-146
  8. Porter T. Some Categorical Results in the Theory of Crossed Modules in Commutative Algebras, Journal of Algebra, 1987; 109; 415-429
  9. Porter T. The Crossed Menagerie: An Introduction to Crossed Gadgetry and Cohomology in Algebra and Topology,
  10. Whitehead JHC. Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 1949: 55; 231-245 and 453-456.