Crossed Corner and Reduced Simplicial Commutative Algebras

Özgün Gürmen Alansal

doi:10.53570/jnt.1391397

EN

Crossed Corner and Reduced Simplicial Commutative Algebras

Abstract

In this paper, we describe the crossed corner of commutative algebras and present the relation between the category of crossed corners of commutative algebras and the category of reduced simplicial commutative algebras with Moore complex of length 2. We provide a passage from crossed corners to bisimplicial algebras. In this construction, we utilize the Artin-Mazur codiagonal functor from reduced bisimplicial algebras to simplicial algebras and the hypercrossed complex pairings in the Moore complex of a simplicial algebra. Using the coskeleton functor from the category of $k$-truncated simplicial algebras to the category simplicial algebras with Moore complex of length $k$, we see that the length of Moore complex of the reduced simplicial algebra obtained from a crossed corner is 2.

Keywords

Crossed modules, simplicial algebras, crossed corner

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory, Topology

Journal Section

Research Article

Authors

Özgün Gürmen Alansal ^*
0000-0003-2851-986X
Türkiye

Early Pub Date

December 30, 2023

Publication Date

December 31, 2023

Submission Date

November 15, 2023

Acceptance Date

December 15, 2023

Published in Issue

Year 2023 Number: 45

DOI

https://doi.org/10.53570/jnt.1391397

IZ

https://izlik.org/JA45HE55HJ

APA

Gürmen Alansal, Ö. (2023). Crossed Corner and Reduced Simplicial Commutative Algebras. Journal of New Theory, 45, 95-104. https://doi.org/10.53570/jnt.1391397

AMA

1.Gürmen Alansal Ö. Crossed Corner and Reduced Simplicial Commutative Algebras. JNT. 2023;(45):95-104. doi:10.53570/jnt.1391397

Chicago

Gürmen Alansal, Özgün. 2023. “Crossed Corner and Reduced Simplicial Commutative Algebras”. Journal of New Theory, nos. 45: 95-104. https://doi.org/10.53570/jnt.1391397.

EndNote

Gürmen Alansal Ö (December 1, 2023) Crossed Corner and Reduced Simplicial Commutative Algebras. Journal of New Theory 45 95–104.

IEEE

[1]Ö. Gürmen Alansal, “Crossed Corner and Reduced Simplicial Commutative Algebras”, JNT, no. 45, pp. 95–104, Dec. 2023, doi: 10.53570/jnt.1391397.

ISNAD

Gürmen Alansal, Özgün. “Crossed Corner and Reduced Simplicial Commutative Algebras”. Journal of New Theory. 45 (December 1, 2023): 95-104. https://doi.org/10.53570/jnt.1391397.

JAMA

1.Gürmen Alansal Ö. Crossed Corner and Reduced Simplicial Commutative Algebras. JNT. 2023;:95–104.

MLA

Gürmen Alansal, Özgün. “Crossed Corner and Reduced Simplicial Commutative Algebras”. Journal of New Theory, no. 45, Dec. 2023, pp. 95-104, doi:10.53570/jnt.1391397.

Vancouver

1.Özgün Gürmen Alansal. Crossed Corner and Reduced Simplicial Commutative Algebras. JNT. 2023 Dec. 1;(45):95-104. doi:10.53570/jnt.1391397

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Crossed Corner of Lie Algebras

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