Abstract
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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.