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Fig. 3.2
Obtained partial
morphism
These two morphisms are represented by the trees
f
T
and
g
T
and their sequential
composition by
h
T
in Fig.
3.1
.
From the point of view based on the information fluxes of these morphisms,
the composition of morphisms
h
C
can be graphically repre-
sented as
a part of the tree h
T
in Fig.
3.2
. It only provides the strict infor-
mation contribution from the object
A
(i.e., the source) into the object
C
(tar-
get of this composed morphism). Hence
∂
0
(f )
=
g
◦
f
:
A
−→
={
a
1
,a
2
,a
3
,a
4
,a
5
}
,
∂
1
(f )
=
{
b
1
,b
2
,b
3
,b
6
}
,
∂
0
(g)
={
b
1
,b
2
,b
3
,b
4
,b
5
}
,
∂
1
(g)
={
c
1
,c
2
,c
3
}
, while
∂
0
(h)
=
∂
0
(g
∂
1
(g)
.
Let us consider, for example, the composition of the c-arrow
h
:
C
−→
D
with
the composed arrow
g
◦
f)
={
a
1
,a
2
,a
3
,a
4
}=
∂
0
(f )
,
∂
1
(h)
=
∂
1
(g
◦
f)
={
c
1
,c
2
,c
3
}=
◦
={
d
1
,...,d
4
}
=
f
in the previous example, where
D
,
h
{
q
C
1
,q
C
2
,q
C
3
,q
⊥
}
,
∂
0
(q
C
1
)
={
c
2
}
,
∂
1
(q
C
1
)
={
d
1
}
,
∂
0
(q
C
2
)
={
c
1
,c
2
,c
3
}
,
∂
1
(q
C
2
)
={
d
2
}
,
∂
0
(q
C
3
)
={
c
1
,c
4
}
,
∂
1
(q
C
3
)
={
d
3
}
,
=
q
B
2
·{
q
A
2
,q
A
3
}
=
q
B
1
·{
−}
with
q
B
2
(tree)
a partial
(incomplete) component of this tree, as represented in Fig.
3.2
. A composition of
(complete) morphisms generally produces a partial (incomplete) morphism (only
a part of the tree
h
T
represents a real contribution from
A
into
C
) with
hidden
a complete and
q
B
1
(tree)
q
A
1
,
