Search results
Results from the WOW.Com Content Network
The intuitive meaning of a stack is that it is a fibred category such that "all possible gluings work". The specification of gluings requires a definition of coverings with regard to which the gluings can be considered. It turns out that the general language for describing these coverings is that of a Grothendieck topology.
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory.Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves, and the moduli stack of elliptic curves.
Stack (geology), a large vertical column of rock in the sea; Stack (mathematics), a sheaf that takes values in categories rather than sets; Algebraic stack, a special kind of stack commonly used in algebraic geometry Stacks Project, an open source collaborative mathematics textbook writing project
Similarly to a stack of plates, adding or removing is only practical at the top. Simple representation of a stack runtime with push and pop operations. In computer science, a stack is an abstract data type that serves as a collection of elements with two main operations: Push, which adds an element to the collection, and
The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry needed to define them".
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold, or n {\displaystyle n} -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n {\displaystyle ...
These reformulations of the definitions of prestacks and stacks make intuitive meanings of those concepts very explicit: (1) "fibered category" means one can construct a pullback (2) "prestack in groupoids" additionally means "locally isomorphic" implies "isomorphic" (3) "stack in groupoids" means, in addition to the previous properties, a ...