User:Fropuff/Drafts/Endofunctor

Official page: Endofunctor

In mathematics, an endofunctor is a functor from a category to itself.

Endofunctor category

For a given category ${\mathcal {C}}$ the class of all endofunctors ${\mathcal {C}}\to {\mathcal {C}}$, with natural transformations between them, forms a category called the endofunctor category of ${\mathcal {C}}$ and denoted $\operatorname {End} ({\mathcal {C}})$. It is a special case of a functor category.

See also

• F-algebra
• Initial algebra
• Monad