Skew category, Galois covering and smash product of a $k$-category

Se p 20 04 Skew category , Galois covering and smash product of a k - category ∗

In this paper we consider categories over a commutative ring provided either with a free action or with a grading of a not necessarily finite group. We define the smash product category and the skew category and we show that these constructions agree with the usual ones for algebras. In case of the smash product for an infinite group our construction specialized for a ring agrees with M. Beatti...

Category Theory and Galois Theory

Galois theory translates questions about fields into questions about groups. The fundamental theorem of Galois theory states that there is a bijection between the intermediate fields of a field extension and the subgroups of the corresponding Galois group. After a basic introduction to category and Galois theory, this project recasts the fundamental theorem of Galois theory using categorical la...

Category of Polygroup Objects

On the category of geometric spaces and the category of (geometric) hypergroups

‎In this paper first we define the morphism between geometric spaces in two different types‎. ‎We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎The relation between hypergroups and geometric spaces is studied‎. ‎By constructing the category $qh$ of $H_{v}$-groups we answer the question...

Category O over Skew Group Rings

We study the BGG Category O over a skew group ring, involving a finite group acting on a regular triangular algebra. We relate the representation theory of the algebra to Clifford theory for the skew group ring, and obtain results on block decomposition, semisimplicity, and enough projectives. O is also shown to be a highest weight category; the BGG Reciprocity formula is slightly different bec...