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 $C_{n}$.
@article{10_37236_2772,
author = {Will Grilliette and Deborah E. Seacrest and Tyler Seacrest},
title = {On blow-ups and injectivity of quivers},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {2},
doi = {10.37236/2772},
zbl = {1266.05099},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2772/}
}
TY - JOUR
AU - Will Grilliette
AU - Deborah E. Seacrest
AU - Tyler Seacrest
TI - On blow-ups and injectivity of quivers
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2772/
DO - 10.37236/2772
ID - 10_37236_2772
ER -
%0 Journal Article
%A Will Grilliette
%A Deborah E. Seacrest
%A Tyler Seacrest
%T On blow-ups and injectivity of quivers
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2772/
%R 10.37236/2772
%F 10_37236_2772
Will Grilliette; Deborah E. Seacrest; Tyler Seacrest. On blow-ups and injectivity of quivers. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/2772
