- maps
between spaces. Nowadays,
functors are used
throughout modern mathematics to
relate various categories. Thus,
functors are
important in all
areas within...
-
relationship that two
functors may exhibit,
intuitively corresponding to a weak form of
equivalence between two
related categories. Two
functors that
stand in...
-
between objects) give rise to
important functors to the
category of sets.
These functors are
called hom-
functors and have
numerous applications in category...
-
contravariant functor acts as a
covariant functor from the
opposite category Cop to D. A
natural transformation is a
relation between two
functors.
Functors often...
- up
functor in Wiktionary, the free dictionary. A
functor, in mathematics, is a map
between categories.
Functor may also
refer to:
Predicate functor in...
- used:
trait Functor[F[_]] { def map[A,B](a: F[A])(f: A => B): F[B] }
Functors form a base for more
complex abstractions like
applicative functors, monads...
- of
adjoint functors is that
every right adjoint functor is
continuous and
every left
adjoint functor is cocontinuous.
Since adjoint functors exist in abundance...
-
addition to
those functors that
delete some of the operations,
there are
functors that
forget some of the axioms.
There is a
functor from the category...
- same as a
contravariant functor from O ( X ) {\displaystyle O(X)} to C {\displaystyle C} .
Morphisms in this
category of
functors, also
known as natural...
- the
category of
contravariant functors from D {\displaystyle D} to the
category of sets; such a
contravariant functor is
frequently called a presheaf...
