Database Reference
In-Depth Information
Fig. 3.1
Composed tree
=
q
B
j
(tree)
|
q
B
j
∈
α
∗
(
M
BC
)
where
q
A
i
(tree)
is the tree bellow the branch
q
A
i
.
The difference between this graphical tree-representation of morphisms in
Fig.
3.1
and of a standard operads-based representation is that in the graphical
tree-representation, for the relations in
∂
0
(h)
that are not relations in
∂
0
(f )
(called
hidden relations
), we do not use the identity functions
α(
1
r
)
for these hidden re-
lations (relations that are not in the source database
A
but in some intermediate
database as 1
Over
65
in Example
8
or 1
Over
65
and 1
Emp
in Example
9
). Let us consider
the following example in order to facilitate the understanding of the composition of
morphisms:
Example 18
Let us consider the morphisms
f
:
A
−→
B
and
g
:
B
−→
C
such
that
A
={
a
1
,...,a
6
}
,
B
={
b
1
,...,b
7
}
,
C
={
c
1
,...,c
4
}
,
={
q
A
1
,...,q
A
4
,q
⊥
}
where
f
with
∂
0
(q
A
1
)
={
a
1
,a
2
}
,
∂
0
(q
A
2
)
={
a
2
,a
3
}
,
∂
0
(q
A
3
)
={
a
4
}
,
∂
0
(q
A
4
)
={
a
4
,a
5
}
,
={
b
1
}
={
b
2
}
∂
1
(q
A
1
)
,
∂
1
(q
A
2
)
,
={
b
3
}
={
b
6
}
∂
1
(q
A
3
)
,
∂
1
(q
A
4
)
and
g
={
q
B
1
,...,q
B
3
,q
⊥
}
with
∂
0
(q
B
1
)
={
b
1
,b
4
}
,
∂
0
(q
B
2
)
={
b
2
,b
3
}
,
∂
0
(q
B
3
)
={
b
4
,b
5
}
,
∂
1
(q
B
1
)
={
c
1
}
,
∂
1
(q
B
2
)
={
c
2
}
,
∂
1
(q
B
3
)
={
c
3
}
.
