Properties
Compact closed categories are a special case of monoidal closed categories, which in turn are a special case of closed categories.
Compact closed categories are precisely the symmetric autonomous categories. They are also *-autonomous.
Every compact closed category C admits a trace. Namely, for every morphism, one can define
which can be shown to be a proper trace.
Read more about this topic: Compact Closed Category
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)