
Algebraic Topology, Category Theory and Higher Dimensional Algebra

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Algebraic Topology vol.1B[edit]

Algebraic Topology, Category Theory and Higher Dimensional Algebra[edit]

Algebraic Topology: Table of contents
Main article: Algebraic topology; Group; Groupoid; Lie groupoid; Crossed module; Galois theory; Topology; Open set; Topological property; Tangent space; Hausdorff space; Metric space-Riemannian space; Riemannian manifold; Fundamental group; Homotopy; Homology (mathematics); Homology group; Cohomology group; Homology theory; Cohomology theory; Homological algebra; Algebraic K-theory; Topological K-theory; Esquisse d'un Programme; Quantum theory; Observable; Wave function; Clifford algebra; Von Neumann algebra; Operator algebra; Hamiltonian; Schrodinger equation; Quantum field theory; Local quantum field theory; Algebraic quantum field theory; Geometrodynamics; Soliton-Quantum Solitons; Spin group; Quantum group; Quantum torus; Spin network; Spin foam; Twistor; Topological quantum field theory; Standard Model; Quantum gravity; Noncommutative geometry; Quantum geometry
Important Theorems in Algebraic Topology;: Borsuk-Ulam theorem; Brouwer fixed point theorem; Cellular approximation theorem; Eilenberg–Zilber theorem; Hurewicz theorem; Künneth theorem; Poincaré duality theorem; Universal coefficient theorem; Van Kampen's theorem; Whitehead's theorem; List of publications in mathematics
Supporting articles: Algorithm; Category theory; Algebraic category; Algebraic logic; Categorical logic; Category (mathematics); Abelian category; Topos; Heyting algebra; Subobject classifier; Generator; Exact sequence; Pushout; Pullback; Sheaf (mathematics); Limit Functor; Colimit; Yoneda lemma; Functor; Adjoint functor; Representable functor; Functor category; Natural equivalence; Natural transformation; Dual (category theory); Isomorphism; Semigroup; Monoid; Higher dimensional algebra; Higher category theory; Enriched category; Graph theory; Colored graph; Multicategory; Metatheory; Metamathematics; Variety

Notable Algebraic Topologists and Category Theoreticians: Michael Atiyah; Nicolas Bourbaki; Karol Borsuk; Ronald Brown (mathematician); Alain Connes; Jean Dieudonne; Otto Hermann Künneth; Charles Ehresmann; Samuel Eilenberg; Peter J. Freyd; Alexander Grothendieck; Heinz Hopf; Saunders Mac Lane; Egbert van Kampen; Roger Penrose; Grigori Perelman; Nicolae Popescu; Nicolas Rashevsky; Robert Rosen; Jean-Pierre Serre; J. H. C. Whitehead; Edward Witten