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:
“It is impossible that anything so natural, so necessary, and so universal as death should ever have been designed by Providence as an evil to mankind.”
—Jonathan Swift (1667–1745)
“The charming landscape which I saw this morning is indubitably made up of some twenty or thirty farms. Miller owns this field, Locke that, and Manning the woodland beyond. But none of them owns the landscape. There is property in the horizon which no man has but he whose eye can integrate all parts, that is, the poet. This is the best part of these men’s farms, yet to this their warranty-deeds give no title.”
—Ralph Waldo Emerson (1803–1882)