# Book:Algebraic Mathematics and Logics

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## Algebraic Logic and Algebraic Mathematics[edit]

- Algebraic Logic
- Boolean algebra
- Algebraic logic
- Łukasiewicz logic
- Intuitionistic logic
- Mathematical logic
- Heyting arithmetic
- Metatheory
- Metalogic

- Quantum Logics and Quantum Computers
- Many-valued logic
- Quantum logic
- Quantum computer

- Abstract Algebra
- Abstract algebra
- Universal algebra
- Heyting algebra
- MV-algebra
- Group algebra
- Lie algebra
- Affine Lie algebra
- Lie group
- Algebroid

- Quantum Algebra and Geometry
- Quantum affine algebra
- Clifford algebra
- Von Neumann algebra
- C*-algebra
- Kac–Moody algebra
- Hopf algebra
- Quantum group
- Group representation
- Unitary representation
- Representation theory of the Lorentz group
- Stone–von Neumann theorem
- Peter–Weyl theorem
- Quasi-Hopf algebra
- Quasitriangular Hopf algebra
- Ribbon Hopf algebra
- Quasi-triangular Quasi-Hopf algebra
- Quantum inverse scattering method
- Yangian
- Exterior algebra
- Superalgebra
- Supergroup
- Noncommutative quantum field theory
- Standard Model
- Noncommutative standard model
- Noncommutative geometry

- Algebraic Geometry and Analytic Geometry
- Algebraic geometry
- List of algebraic geometry topics
- Duality
- Universal algebraic geometry
- Grothendieck topology
- Grothendieck–Hirzebruch–Riemann–Roch theorem
- Algebraic geometry and analytic geometry
- Differential geometry

- Algebraic Topology, Group Theory and Groupoids
- Algebraic topology
- Groupoid
- Group theory
- Abelian group
- Galois group
- Grothendieck group
- Esquisse d'un Programme
- Galois theory
- Grothendieck's Galois theory
- Galois cohomology
- Homological algebra
- Homology theory
- Homotopical algebra
- De Rham cohomology
- Crystalline cohomology
- Cohomology
- K-theory
- Algebraic K-theory
- Topological K-theory

- Category Theory and Categorical Logic
- Category theory
- Category
- Glossary of category theory
- Dual
- Abelian category
- Functor
- Yoneda lemma
- Limit
- Adjoint functors
- Natural transformations
- Variety
- Domain theory
- Enriched category
- Topos
- Descent
- Stack
- Categorical logic
- Timeline of category theory and related mathematics
- List of important publications in mathematics

- Higher Dimensional Algebras
- Higher-dimensional algebra
- Higher category theory
- Duality