Properties
Compact closed categories are *-autonomous, with the dual of the monoidal unit as the dualizing object, but *-autonomous categories need not to be compact closed: is not necessarily a dual of . However, if in a *-autonomous category we have
- .
for each pair (A,B) of objects, then the category is compact closed.
Read more about this topic: *-autonomous Category
Famous quotes containing the word properties:
“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)
“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)