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## Coarse graining presheaf G

**Definition 2.4**

*A*

**coarse graining presheaf**on the category of bounded self adjoints operators (see Category of self-acjoint operators. ) is the contravariant functor 3.2 such that- each object
gets mapped to its spectral algebra
i.e.

- given an
-map
the corresponding function
in G is
such that

or alternatively

where and

for and

*Proof*.

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**Previous:**Coarse Graining Presheaf Cecilia Flori 2007-01-02