PlanetPhysics/Topic on Axioms and Foundations of Homology and Cohomology Theories

Axioms for Homology and Cohomology theories

 * 1) Axioms for homology theory and uniqueness theorems #Cech types #$$K$$-theory
 * 2) Generalized cohomology
 * 3) Generalized (extraordinary) homology and cohomology theories
 * 4) Galois Cohomology and Categorical Galois theories
 * 5) (Co)homology of commutative rings and algebras (e.g., Hochschild, Andr\'e-Quillen, cyclic, dihedral, etc.)
 * 6) Bordism and cobordism theories, formal group laws
 * 7) Homology with local coefficients, equivariant cohomology
 * 8) Sheaf cohomology
 * 9) Cohomology in noncommutative algebraic geometry
 * 10) Classifying spaces for foliations; Gelfand-Fuks cohomology
 * 11) Intersection homology and cohomology
 * 12) Elliptic cohomology
 * 13) Equivariant homology and cohomology
 * 14) Homology and homotopy of topological groups and related structures
 * 15) Homotopy quantum field theories and Axiomatic Quantum Field Theories
 * 16) non-Abelian Homological Algebra
 * 17) Grothendieck's `Anabelian Geometry' #Other homology theories--Your new additions

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