Stack (descent theory)
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High Quality Content by WIKIPEDIA articles! In mathematics a stack is a concept used to formalise some of the main constructions of descent theory. Descent theory is concerned with generalisations of situations where geometrical objects (such as vector bundles on topological spaces) can be "glued together" when they are isomorphic (in a compatible way) when restricted to intersections of the sets in an open covering of a space. In more general set-up the restrictions are replaced with general pull-backs, and fibred categories form the right framework to discuss the possibility of such "glueing...
High Quality Content by WIKIPEDIA articles! In mathematics a stack is a concept used to formalise some of the main constructions of descent theory. Descent theory is concerned with generalisations of situations where geometrical objects (such as vector bundles on topological spaces) can be "glued together" when they are isomorphic (in a compatible way) when restricted to intersections of the sets in an open covering of a space. In more general set-up the restrictions are replaced with general pull-backs, and fibred categories form the right framework to discuss the possibility of such "glueing". The intuitive meaning of a stack is that it is a fibred category such that "all possible glueings work". The specification of glueings requires a definition of coverings with regard to which the glueings can be considered.
