2016/04/20 by Adnan H. Abdulwahid, Abdulwahid, Adnan H.
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1604.05801
openalex publication_date 2016/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We have two parallel goals of this paper. First, we investigate and construct cofree coalgebras over n-representations of quivers, limits and colimits of n-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of n-representations of quivers. Second, we introduce a generalization for quivers and show that this generalization can be seen as essentially the same as n-representations of quivers. This is significantly important because it allows us to build a new quiver \mathscrQ_ (\Qq1, \Qq2,..., \Qqn), called n-quiver, from any given quivers \Qq1,\Qq2,...,\Qqn, and enable us to identify each category Repk(\Qqj) of representations of a quiver \Qqj as a full subcategory of the category Repk(\mathscrQ_ (\Qq1, \Qq2,..., \Qqn)) of representations of \mathscrQ_ (\Qq1, \Qq2,..., \Qqn) for every j ∈ \1, 2, ..., n\.