TY - JOUR
ID - 63576
TI - A Universal Investigation of $n$-representations of $n$-quivers
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Abdulwahid, Adnan
AD - Mathematics Department, College of Computer Sciences and Mathematics, University of Thi-Qar, Iraq
Y1 - 2019
PY - 2019
VL - 10
IS - 1
SP - 69
EP - 106
KW - Quiver
KW - Representation
KW - birepresentation
KW - $n$-representation
KW - additive category
KW - abelian category
KW - $k$-linear category
DO - 10.29252/cgasa.10.1.69
N2 - \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 $j \in \{1,2,\ldots , n\}$.
UR - https://cgasa.sbu.ac.ir/article_63576.html
L1 - https://cgasa.sbu.ac.ir/article_63576_d0e433b72b5f2ad887b121defa6a4a09.pdf
ER -