A Universal Investigation of $n$-representations of $n$-quivers

A Universal Investigation of $n$-representations of $n$-quivers

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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, Nattokinase 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 Wooden Photo Box 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 $j in {1,2,ldots , n}$.