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Algebraic Topology Algebraic Topology, Category Theory and Higher Dimensional Algebra-Results and Applications to Quantum Physics

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Algebraic Topology[edit]

Algebraic Topology, Category Theory and Higher Dimensional Algebra-Results and Applications to Quantum Physics[edit]

Algebra: Algebra; Abstract Algebra; Algebraic logic; Galois group; Galois theory; Grothendieck's Galois theory
Algebraic Topology: Table of contents; Algebraic topology; Open sets; Topology; Topological property; Topological space; Continuous function (topology); Fibration; Homeomorphism; Compact space; Hausdorff space; Tangent space; Metric space-Riemann space; Riemannian manifold; Kähler manifold; Calabi–Yau manifold; Pseudo-Riemannian manifold; Hypersurface; CR manifold; Symplectic manifold; Betti number; Euler characteristics; Presheaf (category theory); Sheaf (mathematics); Postnikov system; Grothendieck topology; Groupoid; Lie groupoid; Lie algebroid; Algebroid; Space group; Fundamental group; Homotopy; Crossed module; Homology (mathematics); Cohomologygroup; Homology theory; Chain complex; Crystalline cohomology; Homological algebra; Algebraic K-theory; Topological K-theory; Stack (descent theory); Esquisse d'un Programme
Important Theorems in Algebraic Topology: Hairy ball theorem; Universal coefficient theorem; Borsuk-Ulam theorem; Brouwer fixed point theorem; Cellular approximation theorem; Eilenberg–Zilber theorem; Hurewicz theorem; Künneth theorem; Poincaré duality theorem; Tychonoff's theorem; Tietze extension theorem; Universal coefficient theorem; Seifert–van Kampen theorem; Whitehead theorem; List of important publications in mathematics
Higher Dimensional Algebra: Higher-dimensional algebra; Higher category theory; Enriched category; Graph theory; Graph coloring-Colored graph; Multicategory; Metatheory; Metalogic; Metamathematics
Category theories: Category theory; Algebraic category; Categorical logic; Category (mathematics); Abelian category; Topos; Heyting algebra; Subobject classifier; Generator; Exact sequence; Coproduct-Direct sum; Product; Pushout; Pullback; Limit; Colimit; Yoneda lemma; Functor; Adjoint functors; Representable functor; Functor category; Natural equivalence; Natural transformation; Dual (category theory); Isomorphism; Semigroup; Monoid; Domain theory; Baire category theorem
Algebraic Quantum Topology: Lagrangian mechanics; Hamiltonian mechanics; Noether's theorem; Quantum theory; Observable; Wave function; Rigged Hilbert space; Kac–Moody algebra; Operator algebra; Clifford algebra; von Neumann algebra; C*-algebra; Jones polynomial; Subfactor(Jones); Quantum logic; Quantum group; Hopf algebra; Quasitriangular Hopf algebra; Quantum doubleconstruction; Grassman algebra; Special unitary group(SUn); Gauge theory; Yang–Mills theory; Yangian; Superalgebra; Supergroup; Symmetry breaking; Spontaneous symmetry breaking; Goldstone bosons; Higgs boson; Higgs mechanism; Topological order; Topological quantum field theory(TQFT); Noncommutative geometry(NCG); Noncommutative quantum field theory; Noncommutative standard model; Quantum geometry; Fuzzy spheres; Quantum torus-tori; Geometrodynamics; Quantum gravity; Homological mirror symmetry-Conjecture
Notable Algebraic Topologists and Category Theoreticians: Michael Atiyah-(Sir); Karol Borsuk; Nicolas Bourbaki; Ronald Brown (mathematician); Henri Cartan; Alain Connes; Jean Dieudonné; Charles Ehresmann; Samuel Eilenberg; Peter J. Freyd; Alexander Grothendieck; Heinz Hopf; Egbert van Kampen; Maxim Kontsevich; Otto Hermann Künneth; Saunders Mac Lane; William Lawvere; Barry Mitchell; Roger Penrose; Grigori Perelman; Nicolae Popescu; Nicolas Rashevsky; Robert Rosen; Jean-Pierre Serre; J. H. C. Whitehead; Edward Witten