Vipul: New page: ==Definition== Suppose $\mathcal{C}$ is a category and $\mathcal{F}:\mathcal{C} \to \operatorname{Set}$ is a contravariant functor to the [[category of sets]...

2008-12-09T23:36:05Z

New page: ==Definition== Suppose <math>\mathcal{C}</math> is a category and <math>\mathcal{F}:\mathcal{C} \to \operatorname{Set}</math> is a contravariant functor to the [[category of sets]...

New page

==Definition==

Suppose <math>\mathcal{C}</math> is a [[category]] and <math>\mathcal{F}:\mathcal{C} \to \operatorname{Set}</math> is a [[contravariant functor]] to the [[category of sets]]. We say that <math>\mathcal{F}</math> is '''representable''' if there exists a [[natural isomorphism]] between <math>\mathcal{F}</math> and the [[contravariant Hom functor]] corresponding to some object <math>A \in \operatorname{Ob}\mathcal{C}</math>.

There is a related notion of [[representable functor]], used for (covariant) functors.

Representable contravariant functor - Revision history

Vipul: New page: ==Definition== Suppose \mathcal{C} is a category and \mathcal{F}:\mathcal{C} \to \operatorname{Set} is a contravariant functor to the [[category of sets]...

Vipul: New page: ==Definition== Suppose $\mathcal{C}$ is a category and $\mathcal{F}:\mathcal{C} \to \operatorname{Set}$ is a contravariant functor to the [[category of sets]...