Homotopy Type Theory Boolean dagger 2-poset > history (Rev #5, changes)

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Contents

Idea

A Boolean dagger 2-poset is a dagger 2-poset whose category of maps is an Boolean category?.

Definition

A Boolean dagger 2-poset $C$ is a Heyting dagger 2-poset where for each objects $A:Ob(C)$, $B:Ob(C)$ and functional dagger monomorphism$i_{B,A}:Hom(B,A)$monic map , there is a$i_{B,A}:Hom(B,A)$, there is a unitary isomorphism $j_{B,A}:A \cong^\dagger B \cup (B \Rightarrow 0)$.

Properties

• The unitary isomorphism classes of functional monic dagger maps monomorphisms into every object$A$ is a Boolean algebra? . Since every functional monic dagger map monomorphism is a map, thecategory of maps is a Boolean category?.

Examples

The dagger 2-poset of decidable sets and relations is an Boolean dagger 2-poset.

See also

• dagger 2-poset
• conjunctive dagger 2-poset
• coherent dagger 2-poset
• geometric dagger 2-poset
• Heyting dagger 2-poset
• Boolean dagger 2-poset
• Boolean topical dagger 2-poset