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A Boolean dagger 2-poset is a dagger 2-poset whose category of maps is an Boolean category?.
A Boolean dagger 2-poset is a Heyting dagger 2-poset where for each objects , and functional dagger monomorphism , there is a unitary isomorphism .
The dagger 2-poset of decidable sets and relations is an Boolean dagger 2-poset.