Pullback Crossed Modules in the Category of Racks
نویسندگان
چکیده
منابع مشابه
The category of generalized crossed modules
In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate som...
متن کاملpullback crossed modules of algebroids*
in this paper, we present algebroids and crossed modules of algebroids. we also define pullbackcrossed module of algebroids.
متن کاملLimits in modified categories of interest
We firstly prove the completeness of the category of crossed modules in a modified category of interest. Afterwards, we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows. These constructions unify many corresponding results for the cases of groups, commutative algebras and can also be adapted to ...
متن کاملOn the Non–balanced Property of the Category of Crossed Modules in Groups
An algebraic category C is called balanced if the cotriple cohomology of any object of C vanishes in positive dimensions on injective coefficient modules. Important examples of balanced and of non-balanced categories occur in the literature. In this paper we prove that the category of crossed modules in groups is non-balanced.
متن کاملRacks, Leibniz algebras and Yetter–Drinfel’d modules
A Hopf algebra object in Loday and Pirashvili’s category of linear maps entails an ordinary Hopf algebra and a Yetter–Drinfel’d module. We equip the latter with a structure of a braided Leibniz algebra. This provides a uni ed framework for examples of racks in the category of coalgebras discussed recently by Carter, Crans, Elhamdadi and Saito.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hacettepe Journal of Mathematics and Statistics
سال: 2017
ISSN: 1303-5010
DOI: 10.15672/hjms.2017.532