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A
-category ,
, is defined as a (small)
2-category for which the following conditions hold:
- for each pair of
-arrows
the space
is a complex Banach space.
- there is an anti-linear involution `
' acting on
-arrows, that is,
,
, with
and
being
-arrows;
- the Banach norm is sub-multiplicative (that is,
, when the composition is defined,
and satisfies the
-condition:
- for any 2-arrow
,
is a positive element in
, (denoted also as
).
Note:
The set of
-arrows
is a commutative monoid, with the identity map
assigning to each object
a
-arrow
such that