Biology Reference
In-Depth Information
M
/
E
M
/
E
1
2
M
/
E
M
/
E
3
4
Figure 4
Four partitions induced by observables. All observables are mutually unlinked
with the exception of
3
and
4
.
such that for every object O and every family of morphisms
f
i
O
→
M/E
i
there is a unique morphism, that is a map, fO
→
P such that for the composition
of the maps
i
and f
i
f
=
f
i
for all i, and
fq
=
f
1
qf
2
qf
i
q
for every q in O. We can summarise the analysis
a
M of M as a direct product
in form of a commutative diagram
O
f
i
f
P=
i
M
/
E
i
M
/
E
i
π
i
In the category of abstract sets and morphisms, named
Set
, the direct product
is the cartesian product; in the category of groups,
Grp
, it is the group direct
product.
Relating the direct product in a general category to the category of analytical
models, we find that for totally unlinked observables there exists an isomorphism
between M and
i
M/E
i
. Considering only two observables,
1
and
2
, the
commutative diagram takes the form
