@article {
author = {Abdulwahid, Adnan},
title = {A Universal Investigation of $n$-representations of $n$-quivers},
journal = {Categories and General Algebraic Structures with Applications},
volume = {10},
number = {1},
pages = {69-106},
year = {2019},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.10.1.69},
abstract = {\noindent We have two goals in 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, for any given quivers $\mathit{Q}_1$,$\mathit{Q}_2$,..., $\mathit{Q}_n$, we construct a new quiver $\mathscr{Q}_{\!_{(\mathit{Q}_1, \mathit{Q}_2,..., \mathit{Q}_n)}}$, called an $n$-quiver, and identify each category $Rep_k(\mathit{Q}_j)$ of representations of a quiver $\mathit{Q}_j$ as a full subcategory of the category $Rep_k(\mathscr{Q}_{\!_{(\mathit{Q}_1, \mathit{Q}_2,..., \mathit{Q}_n)}})$ of representations of $\mathscr{Q}_{\!_{(\mathit{Q}_1, \mathit{Q}_2,..., \mathit{Q}_n)}}$ for every $j \in \{1,2,\ldots , n\}$.},
keywords = {Quiver,Representation,birepresentation,$n$-representation,additive category,abelian category,$k$-linear category},
url = {https://cgasa.sbu.ac.ir/article_63576.html},
eprint = {https://cgasa.sbu.ac.ir/article_63576_d0e433b72b5f2ad887b121defa6a4a09.pdf}
}