16:00
The stable uniqueness theorem for KK-theory asserts that a Cuntz-pair of *-homomorphisms between separable C*-algebras gives the zero element in KK if and only if the *-homomorphisms are stably homotopic through a unitary path, in a specific sense. This result, along with its group equivariant analogue, has been crucial in the classification theory of C*-algebras and C*-dynamics. In this talk, I will present a unitary tensor category analogue of the stable uniqueness theorem and explore its application to a duality in tensor category equivariant KK-theory. To make the talk approachable even for those unfamiliar with actions of unitary tensor categories or KK-theory, I will introduce the relevant definitions and concepts, drawing comparisons with the case of group actions. This is joint work with Kan Kitamura and Robert Neagu.