A constant functor is a functor that maps each object of the category to a fixed object and each morphism of to the identity morphism of that fixed object.
Note that a constant functor can be expressed as the composite
Here is a terminal category (exactly one object and exactly one morphism, namely the identity), and denotes the unique functor from with and .
For any functor, a natural transformation
from a constant functor into is precisely a cone over . Similarly are natural transformation
is a cocone.
Revised on June 20, 2013 12:47:01
by Urs Schreiber