-
morphism on X. Such a
functor is
called a
constant or
selection functor.
Endofunctor A
functor that maps a
category to that same category; e.g., polynomial...
-
concise terms, a
monad is a
monoid in the
category of
endofunctors of some
fixed category (an
endofunctor is a
functor mapping a
category to itself). According...
- {\displaystyle F:{\mathcal {C}}\longrightarrow {\mathcal {C}}} be an
endofunctor on a
category C {\displaystyle {\mathcal {C}}} . An F {\displaystyle...
- F-algebras for a
given endofunctor F. This
initiality provides a
general framework for
induction and recursion.
Consider the
endofunctor 1 + (−), i.e. F :...
- (a two-point
discrete space)
serving as the unit. The
category of all
endofunctors on a
category C is a
strict monoidal category with the
composition of...
- is a category, and F : C → C {\displaystyle F:C\rightarrow C} is an
endofunctor of C {\displaystyle C} , then an F {\displaystyle F} -algebra is a tuple...
- sense, this can be
taken as the
definition of a
limit or colimit. The
endofunctor Hom(E, –) : Set → Set can be
given the
structure of a monad; this monad...
- In algebra, a
polynomial functor is an
endofunctor on the
category V {\displaystyle {\mathcal {V}}} of finite-dimensional
vector spaces that
depends polynomially...
- ****ignment of a
coalgebra to its
unique morphism to the
final coalgebra of an
endofunctor.
These objects are used in
functional programming as unfolds. The categorical...
-
object is a K-coalgebra. For any
category C, the
category [C, C] of its
endofunctors has a
monoidal structure induced by the
composition and the identity...
