Database Reference
In-Depth Information
Corollary 1
A category
C
is symmetric if for its algebra Alg
C
=
((Ob
C
, Mor
C
),
Ob
C
→
Σ
C
) we have the additional binary partial operator
∗:
Ob
C
and unary
operator B
T
∈
Σ
C
which is a homomorphism B
T
:
(Mor
C
,
◦
)
→
(Ob
C
,
∗
) such
that for every object A
∈
Ob
C
there exists the isomorphism
,
B
T
(id(A))
A
(
repre-
sentability principle
).
Notice that the partial operations can be equivalently represented by a set of stan-
dard (total) operations. For example, the partial operation '
◦
' can be equivalently
represented by the set of total operations,
◦
A,B,C
:
OB
C
.
C
(A,B)
×
C
(B,C)
→
C
(A,C)
|
A,B,C
∈
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