An initial object in a category C is an object for which every other object of C is a codomain
of a unique morphism with the initial object as a domain.
In this diagram the classes are represented by rectangles and the relations by arrows (domain towards codomain
) labelled by the name of the relation.
(iii) [F.sub.2] (R), [F.sub.3] (R), [G.sub.2] (R), and [G.sub.3] (R) to be R, where R is considered with the appropriate domain and codomain
However, it presents a drawback highlighted in  and related to the fact that its codomain
is the limited interval (0, [pi]/2); thus its normalizing effect may turn out to be meagre, as already pointed out in some studies where it has been used for estimating the reliability of stress-strength models [19, 25, 26].
The vectors RL and [R.sup.[??]] L are particular vectors characterizing, respectively, the domain and codomain
Thus, an error criterion ci is an onto-function with domain in I, and codomain
Taking every other value of i ensures that the complement of the codomain
is infinite: we will need this in the next step.
K-metric and K-normed spaces were introduced in the mid-20th century (see [2, 16, 24, 26]) by using an ordered Banach space instead of the set of real numbers, as the codomain
for a metric.
Observe that (0,1] is a semi-open set in the codomain
that contains f(1) = 1.
Equivalently, f is a submersion if its differential has constant rank equal to the dimension of the codomain
of f .
The function f(x) is nondecreasing and piecewise linear, and its codomain
is [[l.sub.min], [l.sub.max]].
We thus conclude that the codomain
of [member of] of Definition 4.4 can be extended to the family [[Delta].sup.+.sub.1] of all nondecreasing functions [member of] : [0, +[infinity]] [right arrow] [0, 1] such that F(0) = 0 and E([infinity]) = 1.