morphisms between quivers
Recall that a quadruple is a quiver, if is a set (whose elements are called vertices), is also a set (whose elements are called arrows) and are functions which take each arrow to its source and target respectively.
such that , are functions which satisfy
In this case we write . In other words is a morphism of quivers, if for an arrow
in the following
is an arrow in .
It can be easily checked, that is again a morphism between quivers.
The class of all quivers, all morphisms between together with the composition is a category. In particular we have a notion of isomorphism. It can be shown, that two quivers , are isomorphic if and only if there exists a morphism of quivers
such that both and are bijections.
For example quivers
are isomorphic, although not equal.
|Title||morphisms between quivers|
|Date of creation||2013-03-22 19:16:57|
|Last modified on||2013-03-22 19:16:57|
|Last modified by||joking (16130)|