On the Barr exactness property of $\mathsf{BXMod/R}$

Akay, Hatice Gülsün; Arslan, Ummahan Ege

doi:10.18514/mmn.2018.1695

MMN

2018

DOI: 10.18514/mmn.2018.1695

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On the Barr exactness property of $\mathsf{BXMod/R}$

Hatice Gülsün Akay¹,

Ummahan Ege Arslan²

Abstract: In this work, it is shown that the category BXMod=R of braided crossed modules over a fixed commutative algebra R is an exact category in the sense of Barr.

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2024

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Isomorphism Theorems for Crossed Squares of Commutative Algebras

Çetin,

Can

2024

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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The isomorphism theorems for crossed squares of commutative algebras, which arise when the crossed modules of algebras are given an extra dimension, are the main subject of this paper. The definition of crossed squares of commutative algebras is given in this context, encompassing ideas like the crossed square ideal, image, and quotient crossed squares, as well as the kernel for crossed square morphisms. The study discusses the way how isomorphism theorems are applied to these structures and offers detailed proofs for this framework. Moreover, some necessary concepts such as quotient crossed squares, which were not previously specified in these structures, are also presented, and some basic properties are examined. The study provides opportunities for possible generalization to a number of different structures, including crossed n-cubes.

show abstract

Isomorphism Theorems for Crossed Squares of Commutative Algebras

Çetin,

Can

2024

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi

View full text Add to dashboard Cite

show abstract

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On the Barr exactness property of $\mathsf{BXMod/R}$

Abstract: In this work, it is shown that the category BXMod=R of braided crossed modules over a fixed commutative algebra R is an exact category in the sense of Barr.

Cited by 1 publication

References 8 publications

Isomorphism Theorems for Crossed Squares of Commutative Algebras

Isomorphism Theorems for Crossed Squares of Commutative Algebras

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