characterization of isomorphisms of quivers
is given by , where both and are the identities on , respectively.
Proposition. A morphism of quivers is an isomorphism if and only if both and are bijctions.
,,” Assume that both and are bijections and define and by
Since is a morphism of quivers, then
which implies that
The same arguments hold for the target function , which completes the proof.
|Title||characterization of isomorphisms of quivers|
|Date of creation||2013-03-22 19:17:31|
|Last modified on||2013-03-22 19:17:31|
|Last modified by||joking (16130)|