engleski

Yang-Baxter condition, equivariance and cyclic cohomology

In several situations, constructions of cyclic objects in the sense of Connes involve braidings and equivariant objects of some type. I will briefly sketch several examples, and categorical constructions which fit into this picture: cyclic comonads via Yang-Baxter requirement, connections to the distributive laws, a relation between inertia groupoids and monoidal center, and some comparison to the Hopf-cyclic cohomology with coefficients. I also show several basic constructions needed to properly study equivariance phenomena in noncommutative and categorical setup, for example the 2-categorical analogue of equivariant sheaves.

comonad; inertia groupoid; quantum Yang-Baxter equation; cyclic object; monoidal center; equivariance; distributive laws; cyclic cohomology with coefficients

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