2-Valued Morphism

# 2-valued morphism

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2-valued morphism is a term used in mathematics to describe a morphism that sends a Boolean algebra B onto a two-element Boolean algebra 2 = . It is essentially the same thing as an ultrafilter on B.

A 2-valued morphism can be interpreted as representing a particular state of B. All proposition of B which are mapped to 1 are considered true, all propositions mapped to 0 are considered false. Since this morphism conserves the Boolean operators (negation, conjunction, etc.), the set of true propositions will not be inconsistent but will correspond to a particular maximal conjunction of propositions, denoting the (atomic) state.

The transition between two states s<sub>1</sub> and s<sub>2</sub> of B, represented by 2-valued morphisms, can then be represented by an automorphism f from B to B, such tuhat s<sub>2</sub> o f = s<sub>1</sub>.

The possible states of different objects defined in this way can be conceived as representing potential events. The set of events can then be structured in the same way as invariance of causal structure, or local-to-global causal connections or even formal properties of global causal connections.

The morphisms between (non-trivial) objects could be viewed as representing causal connections leading from one event to another one. For example, the morphism f above leads form event s<sub>1</sub> to event s<sub>2</sub>. The sequences or "paths" of morphisms for which there...

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