Properties
More generally a stack refers to any category acting more or less like a moduli space with a universal family (analogous to a classifying space) parametrizing a family of related mathematical objects such as schemes or topological spaces, especially when the members of these families have nontrivial automorphisms. This leads to the notion that the points of the stack should carry automorphisms themselves, and this in turn gives rise to the notion of a stack as a certain kind of "category fibered in groupoids".
Moduli spaces which do not carry this extra information are then referred to as coarse moduli spaces and stacks then act as relatively fine moduli spaces.
Read more about this topic: Algebraic Stack
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)