topic on axioms and foundations of homology and cohomology theories

Axioms for homology theory and uniqueness theorems
Cech types
K-theory
Generalized cohomology
Generalized (extraordinary) homology and cohomology theories
Galois Cohomology and Categorical Galois theories
(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
Bordism and cobordism theories, formal group laws
Homology with local coefficients, equivariant cohomology
Sheaf cohomology
Cohomology in noncommutative algebraic geometry
Classifying spaces for foliations; Gelfand-Fuks cohomology
Intersection homology and cohomology
Elliptic cohomology
Equivariant homology and cohomology
Homology and homotopy of topological groups and related structures
Homotopy quantum field theories and Axiomatic Quantum Field Theories
non-Abelian Homological Algebra
Grothendieck’s ‘Anabelian Geometry’
Other homology theories–Your new additions

[1] Hatcher, A. 2001. Algebraic Topology (textbook on line)., Cambridge University Press; Cambridge, UK., 405 pages.

[2] Ronald Brown: Topology and Groupoids, BookSurge LLC (2006).

[3] Ronald Brown R, P.J. Higgins, and R. Sivera.: “Non-Abelian algebraic topology”, (2008).

[4] R. Brown and J.-L. Loday: Homotopical excision, and Hurewicz theorems, for n-cubes of spaces, Proc. London Math. Soc., 54:(3), 176-192, (1987).

[5] R. Brown and J.-L. Loday: Van Kampen Theorems for diagrams of spaces, Topology, 26: 311-337 (1987).

[6] R. Brown and C.B. Spencer: Double groupoids and crossed modules, Cahiers Top. Géom. Diff., 17 (1976), 343-362.

[7] Allain Connes: Noncommutative Geometry, Academic Press 1994.

[8] May, J.P. 1999, A Concise Course in Algebraic Topology., The University of Chicago Press: Chicago

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