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Cosa (chi) è representable$69379$ - definizione
FUNCTOR F: C → SET TO THE CATEGORY OF SETS, NATURALLY ISOMORPHIC TO A HOM-FUNCTOR HOM(X, –) FOR SOME OBJECT X IN C
Universal element; Representable presheaf; Representing object
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 category in terms of known structures (i.
Matroid representation
![The [[Perles configuration]], linear over the reals but not the rationals](https://commons.wikimedia.org/wiki/Special:FilePath/Perles configuration.svg?width=200 "The [[Perles configuration]], linear over the reals but not the rationals")
![The [[Vámos matroid]], not linear over any field](https://commons.wikimedia.org/wiki/Special:FilePath/Vamos matroid.svg?width=200 "The [[Vámos matroid]], not linear over any field")
ABSTRACT COMBINATORIAL REPRESENTATION OF LINEARLY INDEPENDENT VECTORS
Linear matroid; Representable matroid
In the mathematical theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations are analogous to group representations; both types of representation provide abstract algebraic structures (matroids and groups respectively) with concrete descriptions in terms of linear algebra.
Succinct game
IN ALGORITHMIC GAME THEORY
Succinctly representable game; Polymatrix game
In algorithmic game theory, a succinct game or a succinctly representable game is a game which may be represented in a size much smaller than its normal form representation. Without placing constraints on player utilities, describing a game of n players, each facing s strategies, requires listing ns^n utility values.
Wikipedia
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 category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings.
From another point of view, representable functors for a category C are the functors given with C. Their theory is a vast generalisation of upper sets in posets, and of Cayley's theorem in group theory.
