# PlanetPhysics/2C Category

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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