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 almost universal bareness and smoothness of the landscape were as agreeable as novel, making it so much more like the deck of a vessel.”
—Henry David Thoreau (1817–1862)
“I must feel pride in my friend’s accomplishments as if they were mine,—and a property in his virtues. I feel as warmly when he is praised, as the lover when he hears applause of his engaged maiden.”
—Ralph Waldo Emerson (1803–1882)