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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.
Download QR code; Print/export ... The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic ...
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
An effective quotient orbifold, e.g., [/] where the action has only finite stabilizers on the smooth space , is an example of a quotient stack. [2]If = with trivial action of (often is a point), then [/] is called the classifying stack of (in analogy with the classifying space of ) and is usually denoted by .
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.
The first nine blocks in the solution to the single-wide block-stacking problem with the overhangs indicated. In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire (Johnson 1955), also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table.
Pursuing Stacks (French: À la Poursuite des Champs) is an influential 1983 mathematical manuscript by Alexander Grothendieck. [1] It consists of a 12-page letter to Daniel Quillen followed by about 600 pages of research notes.
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.