PlanetPhysics/Quantum Logic Topoi

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Quantum logic topoi
A \htmladdnormallink{quantum logic {http://planetphysics.us/encyclopedia/TheoryOfHilbertLattices.html} topos} (QLT ) is defined as an extension of the concept of topos in which the Heyting logic algebra (or subobject classifier) of the standard elementary topos is replaced by a quantum logic which is axiomatically defined by \htmladdnormallink{non-commutative {http://planetphysics.us/encyclopedia/AbelianCategory3.html} and non-distributive} lattice structures.

Remark
Quantum logic topoi are thus generalizations of the Birkhoff and von Neumann definition of quantum state spaces based on their definition of a quantum logic (lattice), as well as a non-Abelian, higher dimensional extension of the recently proposed concept of a 'quantum' topos which employs the (commutative ) Heyting logic algebra as a subobject classifier.

Some specific examples are considered in the following two recent references.