On Blow-Ups and Injectivity of Quivers
Copyright policy )On Blow-Ups and Injectivity of Quivers
This work connects the idea of a "blow-up" of a quiver with that of injectivity, showing that for a class of monic maps $\Phi$, a quiver is $\Phi$-injective if and only if all blow-ups of it are as well. This relationship is then used to characterize all quivers that are injective with respect to the natural embedding of $P_{n}$ into $C_{n}$.
- University of Montana Western United States
- Tyler Junior College United States
05C60, Directed graphs (digraphs), tournaments, Mathematics - Category Theory, directed graph, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), FOS: Mathematics, Mathematics - Combinatorics, Category Theory (math.CT), Combinatorics (math.CO), blow-up, injectivity
05C60, Directed graphs (digraphs), tournaments, Mathematics - Category Theory, directed graph, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), FOS: Mathematics, Mathematics - Combinatorics, Category Theory (math.CT), Combinatorics (math.CO), blow-up, injectivity
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