Gorenstein injective cotorsion pairs in Grothendieck categories are complete precisely when the category admits a set of Tate trivial generators.
P\'erez, Locally type FP_n and n -coherent categories , Appl
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Accessibility and Gorenstein injective envelopes
Gorenstein injective cotorsion pairs in Grothendieck categories are complete precisely when the category admits a set of Tate trivial generators.