Let be a quiver.
Definition. An equivalence relation on is a pair
such that is an equivalence relation on , is an equivalence relation on and if
for some arrows , then
If is an equivalence relation on , then is a quiver, where
This quiver is called the quotient quiver of by and is denoted by .
It can be easily seen, that if is a quiver and is an equivalence relation on , then
Example. Consider the following quiver
If we take by putting and , , then the corresponding quotient quiver is isomorphic to
|Date of creation||2013-03-22 19:17:22|
|Last modified on||2013-03-22 19:17:22|
|Last modified by||joking (16130)|