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In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory, and to construct fine moduli stacks when fine moduli spaces do not exist.
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 ...
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
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.
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
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
Talk: Stack (mathematics) Add languages. Page contents not supported in other languages. Article; Talk; English ...
A gerbe on a topological space [1]: 318 is a stack of groupoids over that is locally non-empty (each point has an open neighbourhood over which the section category of the gerbe is not empty) and transitive (for any two objects and of () for any open set , there is an open covering = {} of such that the restrictions of and to each are connected by at least one morphism).