Abstract We show that if ${\mathcal C}$ is a fusion $2$ -category in which the endomorphism category of unit object or , then indecomposable objects form finite group.

Everyone knows that if you have a bivariant homology theory satisfying base change formula, get an representation of category correspondences. For theories in which the covariant and contravariant transfer maps are mutual adjunction, these data actually equivalent. In other words, 2-category correspondences is universal way to attach given 1-category set right adjoints satisfy formula. Through ...

In this paper we show that to a unital associative algebra object (resp. co-unital coassociative co-algebra object) of any abelian monoidal category (C,⊗) endowed with a symmetric 2-trace, i.e. an F ∈ Fun(C,Vec) satisfying some natural trace-like conditions, one can attach a cyclic (resp. cocyclic) module, and therefore speak of the (co)cyclic homology of the (co)algebra “with coefficients in F...