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A complex $X$ is called Ding injective if there exists an exact sequence ofinjective complexes $\ldots \rightarrow E_1 \rightarrow E_0 \rightarrow E_{-1}\rightarrow \ldots$ such that $X = Ker(E_0 \rightarrow E_{-1})$, and thesequence remains exact when the functor $Hom(A,-)$ is applied to it, for any$FP$-injective complex $A$. We prove that, over any ring $R$, a complex is Dinginjective if and only if it is a complex of Ding injective modules. We use thisto show that the class of Ding injective complexes is enveloping over any ring.

Ding injective envelopes in the category of complexes