On twisted higher-rank graph C*-algebras

We define the categorical cohomology of a k-graph Λ and show

that the first three terms in this cohomology are isomorphic to the corresponding

terms in the cohomology defined in our previous paper. This leads to

an alternative characterisation of the twisted k-graph C∗-algebras introduced

there. We prove a gauge-invariant uniqueness theorem and use it to show

that every twisted k-graph C∗-algebra is isomorphic to a twisted groupoid

C∗-algebra. We deduce criteria for simplicity, prove a Cuntz-Krieger uniqueness

theorem and establish that all twisted k-graph C∗-algebras are nuclear

and belong to the bootstrap class.