Universal Property
A dependency morphism (with respect to a dependency D) is a morphism
to some monoid M, such that the "usual" trace properties hold, namely:
- 1. implies that
- 2. implies that
- 3. implies that
- 4. and imply that
Dependency morphisms are universal, in the sense that for a given, fixed dependency D, if is a dependency morphism to a monoid M, then M is isomorphic to the trace monoid . In particular, the natural homomorphism is a dependency morphism.
Read more about this topic: Trace Monoid
Famous quotes containing the words universal and/or property:
“The philosophers conception of things will, above all, be truer than other mens, and his philosophy will subordinate all the circumstances of life. To live like a philosopher is to live, not foolishly, like other men, but wisely and according to universal laws.”
—Henry David Thoreau (18171862)
“All over this land women have no political existence. Laws pass over our heads that we can not unmake. Our property is taken from us without our consent. The babes we bear in anguish and carry in our arms are not ours.”
—Lucy Stone (18181893)