Functor Category
In category theory, a branch of mathematics, the functors between two given categories form a category, where the objects are the functors and the morphisms are natural transformations between the functors. Functor categories are of interest for two main reasons:
- many commonly occurring categories are (disguised) functor categories, so any statement proved for general functor categories is widely applicable;
- every category embeds in a functor category (via the Yoneda embedding); the functor category often has nicer properties than the original category, allowing certain operations that were not available in the original setting.
Read more about Functor Category: Definition, Examples, Facts
Famous quotes containing the word category:
“I see no reason for calling my work poetry except that there is no other category in which to put it.”
—Marianne Moore (18871972)
Related Phrases
Related Words