Fibred Categories

Some articles on categories, fibred, fibred categories:

Fibred Category - Examples
... Categories of arrows For any category E the category of arrows A(E) in E has as objects the morphisms in E, and as morphisms the commutative squares in E (mor ... Cartesian morphisms in A(E) are precisely the cartesian squares in E, and thus A(E) is fibred over E precisely when fibre products exist in E ... exist in the category Top of topological spaces and thus by the previous example A(Top) is fibred over Top ...
Fibred Category
... Fibred categories are abstract entities in mathematics used to provide a general framework for descent theory ... Fibred categories formalise the system consisting of these categories and inverse image functors ... guises in mathematics, in particular in algebraic geometry, which is the context in which fibred categories originally appeared ...
Fibred Category - Properties - The 2-categories of Fibred Categories and Split Categories
... The categories fibred over a fixed category E form a 2-category Fib(E), where the category of morphisms between two fibred categories F and G is defined to be the category CartE(F ... Similarly the split categories over E form a 2-category Scin(E) (from French catégorie scindée), where the category of morphisms between two split categories F and G is the full sub-category ScinE(F,G) of E-f ... Each such morphism of split E-categories is also a morphism of E-fibred categories, i.e ...

Famous quotes containing the word categories:

    The analogy between the mind and a computer fails for many reasons. The brain is constructed by principles that assure diversity and degeneracy. Unlike a computer, it has no replicative memory. It is historical and value driven. It forms categories by internal criteria and by constraints acting at many scales, not by means of a syntactically constructed program. The world with which the brain interacts is not unequivocally made up of classical categories.
    Gerald M. Edelman (b. 1928)