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\subsection{Axiomatics and Categorical Foundations of Mathematical Physics}
This is a contributed new topic on the mathematical foundations of \htmladdnormallink{theoretical physics}{http://planetphysics.us/encyclopedia/PhysicalMathematics2.html} and \htmladdnormallink{quantum theories}{http://planetphysics.us/encyclopedia/SpaceTimeQuantizationInQuantumGravityTheories.html}.
\begin{enumerate}
\item Axiomatic foundations of quantum field theories
\item \htmladdnormallink{quantum logics}{http://planetphysics.us/encyclopedia/LQG2.html} and logic algebras: Post and $MV$ logics
\item Index of \htmladdnormallink{Quantum Algebraic Topology}{http://planetphysics.us/encyclopedia/TriangulationMethodsForQuantizedSpacetimes2.html} \item \htmladdnormallink{adjointness}{http://planetphysics.us/encyclopedia/DualityAndTriality.html}, equivalence, \htmladdnormallink{isomorphism}{http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html} at the foundations of \htmladdnormallink{categorical physics}{http://planetphysics.us/encyclopedia/CategoricalPhysics2.html} \item \htmladdnormallink{category theory}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} in quantum physics and \htmladdnormallink{general relativity}{http://planetphysics.us/encyclopedia/SR.html} \item \htmladdnormallink{Categories of quantum logic algebras}{http://planetphysics.us/encyclopedia/AlgebraicCategoryOfLMnLogicAlgebras.html}
\item \htmladdnormallink{functor categories}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} and \htmladdnormallink{super-categories}{http://planetphysics.us/encyclopedia/SuperCategory6.html} \item \htmladdnormallink{index of category theory}{http://planetphysics.us/encyclopedia/IndexOfCategoryTheory.html} \item \htmladdnormallink{indexes of category}{http://planetphysics.us/encyclopedia/IndexOfCategories.html}
\item \htmladdnormallink{classification}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} of $C^*$-algebras and \htmladdnormallink{groupoid}{http://planetphysics.us/encyclopedia/GroupoidHomomorphism2.html} \htmladdnormallink{convolution}{http://planetphysics.us/encyclopedia/AssociatedGroupoidAlgebraRepresentations.html} $C^*$-algebras
\item Quantum topoi and quantum logic extended-toposes
\item \htmladdnormallink{non-Abelian}{http://planetphysics.us/encyclopedia/AbelianCategory3.html} structures and gauge theories
\item \htmladdnormallink{Non-Abelian Quantum Algebraic Topology}{http://planetphysics.us/encyclopedia/NonAbelianQuantumAlgebraicTopology3.html} and \htmladdnormallink{AQFT}{http://planetphysics.us/encyclopedia/SUSY2.html} \item Classical and categorical Galois theories of \htmladdnormallink{quantum groups}{http://planetphysics.us/encyclopedia/QuantumGroup4.html} and \htmladdnormallink{quantum groupoids}{http://planetphysics.us/encyclopedia/WeakHopfAlgebra.html}
\item Theory of quantum \htmladdnormallink{computation}{http://planetphysics.us/encyclopedia/LQG2.html}: quantum logics, \htmladdnormallink{quantum automata}{http://planetphysics.us/encyclopedia/QuantumComputers.html} and quantum computation
\item Measure theory and probability in \htmladdnormallink{quantum statistical mechanics}{http://planetphysics.us/encyclopedia/QuantumStatisticalTheories.html} \item \htmladdnormallink{quantum symmetries}{http://planetphysics.us/encyclopedia/HilbertBundle.html} and quantum groupoid \htmladdnormallink{representation}{http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} theory
\item \htmladdnormallink{noncommutative geometry}{http://planetphysics.us/encyclopedia/NoncommutativeGeometry4.html}, \htmladdnormallink{SUSY}{http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html} and axiomatic \htmladdnormallink{quantum gravity}{http://planetphysics.us/encyclopedia/LQG2.html} (AQG)
\item \end{enumerate}
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