Crossed Corner and Reduced Simplicial Commutative Algebras
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 bisi...
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| Format: | Article |
| Language: | English |
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Naim Çağman
2023-12-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3539941 |
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| _version_ | 1849723795973079040 |
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| author | Özgün Gürmen Alansal |
| author_facet | Özgün Gürmen Alansal |
| author_sort | Özgün Gürmen Alansal |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4d7c44e5a15b45b1b8431c11067f08ce |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-4d7c44e5a15b45b1b8431c11067f08ce2025-08-20T03:10:56ZengNaim ÇağmanJournal of New Theory2149-14022023-12-01459510410.53570/jnt.13913972425Crossed Corner and Reduced Simplicial Commutative AlgebrasÖzgün Gürmen Alansal0https://orcid.org/0000-0003-2851-986XKÜTAHYA DUMLUPINAR ÜNİVERSİTESİIn 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.https://dergipark.org.tr/en/download/article-file/3539941crossed modulessimplicial algebrascrossed corner |
| spellingShingle | Özgün Gürmen Alansal Crossed Corner and Reduced Simplicial Commutative Algebras Journal of New Theory crossed modules simplicial algebras crossed corner |
| title | Crossed Corner and Reduced Simplicial Commutative Algebras |
| title_full | Crossed Corner and Reduced Simplicial Commutative Algebras |
| title_fullStr | Crossed Corner and Reduced Simplicial Commutative Algebras |
| title_full_unstemmed | Crossed Corner and Reduced Simplicial Commutative Algebras |
| title_short | Crossed Corner and Reduced Simplicial Commutative Algebras |
| title_sort | crossed corner and reduced simplicial commutative algebras |
| topic | crossed modules simplicial algebras crossed corner |
| url | https://dergipark.org.tr/en/download/article-file/3539941 |
| work_keys_str_mv | AT ozgungurmenalansal crossedcornerandreducedsimplicialcommutativealgebras |