Properties
The history monoid is isomorphic to the trace monoid, and as such, is a type of semi-abelian categorical product in the category of monoids. In particular, the history monoid is isomorphic to the trace monoid with the dependency relation given by
In simple terms, this is just the formal statement of the informal discussion given above: the letters in an alphabet can be commutatively re-ordered past the letters in an alphabet, unless they are letters that occur in both alphabets. Thus, traces are exactly global histories, and vice-versa.
Read more about this topic: History Monoid
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)