Category: Representable functors

Moduli scheme
In mathematics, a moduli scheme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck. Some important moduli problems of algebraic geometry can be satisfactorily
Volodin space
In mathematics, more specifically in topology, the Volodin space of a ring R is a subspace of the classifying space given by where is the subgroup of upper triangular matrices with 1's on the diagonal
Classifying space
In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e. a topological space all of whose homotopy group
Density theorem (category theory)
In category theory, a branch of mathematics, the density theorem states that every presheaf of sets is a colimit of representable presheaves in a canonical way. For example, by definition, a simplicia
Brown's representability theorem
In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy category Hotc of pointed connected CW comple
Yoneda lemma
In mathematics, the Yoneda lemma is arguably the most important result in category theory. It is an abstract result on functors of the type morphisms into a fixed object. It is a vast generalisation o
Representable functor
In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets. Such functors give representations of an abstract categ
Category of elements
In category theory, if C is a category and F:C→Set is a set-valued functor, the category el(F) of elements of F (also denoted ∫CF) is the following category: * Objects are pairs where and . * Morphi