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Transfer Krull monoids are a recent concept including all commutative Krulldomains and also, for example, wide classes of non-commutative Dedekinddomains. We show that transfer Krull monoids are fully elastic (i.e., everyrational number between $1$ and the elasticity of the monoid can be realized asthe elasticity of an element). In commutative Krull monoids which havesufficiently many prime divisors in all classes of their class group, the setof catenary degrees and the set of tame degrees are intervals. Without theassumption on the distribution of prime divisors, arbitrary finite sets can berealized as sets of catenary degrees and as sets of tame degrees.

Sets of Arithmetical Invariants in Transfer Krull Monoids