A Note on Simplicial Groupids

Yıl 2020, Cilt: 36 Sayı: 1, 82 - 87, 26.04.2020

Ali Aytekin

Öz

Showing the equivalence of the two categories is very important in terms of investigating the properties. This equivalence shows that the properties existing in the category exist in the other category without the need to examination. From this point of view, since the category of groupoids is a category better known than the category of simplicial groupoids, thanks to equivalence, all the properties in the category of groupoids are valid for the category of simplicial groupoids. Main objective of this paper is to give simplicial object in category of groupoids and to prove the equivalence between the category of simplicial groupoids and the category of crossed modules over groupoids.

Anahtar Kelimeler

Groupoid, simplicial object, crossed module

Simplisel Grupoidler Üzerine bir not

Öz

İki kategorinin denkliğini göstermek özelliklerin incelenmesi bakımında oldukça önemlidir. Bu denklik, kategoride var olan özelliklerin, incelemeye gerek kalmadan diğer kategoride de var olduğunu gösterir. Bu açıdan bakıldığında grupoidler kategorisi, simplisel grupoidler kategorisine göre daha iyi bilinen bir kategori olduğundan denklik sayesinde grupoidler kategorisindeki özelliklerin tamamı simplisel grupoidler kategorisi için de geçerlidir. Bu makalenin temel amacı grupoidler kategorisinde simplisel objeyi vermek ve simplisel grupoidler kategorisiyle grupoidler üzerinde çaprazlanmış modüller kategorisinin denkliğini göstermektir.

Anahtar Kelimeler

grupoid, simplisel obje, çaprazlanmış modül

Kaynakça

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