Lie Çaprazlanmış Modüllerin Bazı Kategoriksel Özellikleri

Year 2023, Volume: 23 Issue: 6, 1418 - 1427, 28.12.2023

Pınar Küçüker Ali Aytekin

https://doi.org/10.35414/akufemubid.1300509

Abstract

Kategori teorisi, matematiksel yapılar ve bu yapılar arası ilişkiler ile soyut açıdan ilgilenen bir matematik kuramı olarak bilinmektedir. Ayrıca bir cebirsel yapının kategoriksel özelliklerini incelemek, o kategori hakkında detaylı bilgiye sahip olmak adına oldukça önemlidir. Bu makalede, Lie cebirleri ve onun çaprazlanmış modülleri hakkında temel bilgiler verilerek Lie çaprazlanmış modüller kategorisinin bir alt kategorisinde eşitleyici, çarpım, limit, geri çekme, ileri itme gibi bazı kategoriksel özellikler incelenmiştir.

Keywords

Lie Cebirleri, Çaprazlanmış Modüller, Geri Çekme, İleri İtme

Thanks

Bu makale Pamukkale Üniversitesi Fen Bilimleri Enstitüsü öğrencisi Pınar Küçüker'in yüksek lisans tezinden üretilmiştir.

Some Categorical Aspects of Lie Crossed Modules

Abstract

Category theory is known as a mathematical theory that deals abstractly with mathematical structures and the relationships between these structures. In addition, examining the categorical properties of an algebraic structure is very important in order to have detailed information about that category. In this article, elementary properties were given about Lie algebras and their crossed modules. Some categorical aspects such as equalizer, product, limit, pullback, pushout were examined in a subcategory of the category of Lie crossed modules.

Keywords

Lie Algebras, Crossed Modules, Pullback, Pushout

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