Hochschild and cyclic homology of -algebras.
We generalize the notion of cubical homology to the class of locally compact representable sets in order to propose a new convenient method of reducing the complexity of a set while computing its homology.
A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.
Homology functor in the spirit of the AST is defined, its basic properties are studied. Eilenberg-Steenrod axioms for this functor are formulated and established.
The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.