In this paper we show that if the class of -modules is closed under well ordered direct limits, then the class is preenveloping in the category of -modules if and only if the class is preenveloping in the category of -complexes, where denotes the class of all complexes with all components in . As an immediate consequence, we get that over commutative and Noetherian rings with dualizing complexes every complex admits a Gorenstein flat preenvelope.
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Gang Yang, Zhongkui Liu, Li Liang, On Gorenstein Flat Preenvelopes of Complexes. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 171–187