Geodesic
WEAK INJECTIVE AND WEAK FLAT COMPLEXES
Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 539-557

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DOI

Let R be an arbitrary ring. We introduce and study a generalization of injective and flat complexes of modules, called weak injective and weak flat complexes of modules respectively. We show that a complex C is weak injective (resp. weak flat) if and only if C is exact and all cycles of C are weak injective (resp. weak flat) as R-modules. In addition, we discuss the weak injective and weak flat dimensions of complexes of modules. Finally, we show that the category of weak injective (resp. weak flat) complexes is closed under pure subcomplexes, pure epimorphic images and direct limits. As a result, we then determine the existence of weak injective (resp. weak flat) covers and preenvelopes of complexes. 
GAO, ZENGHUI; HUANG, ZHAOYONG. WEAK INJECTIVE AND WEAK FLAT COMPLEXES. Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 539-557. doi: 10.1017/S0017089515000324
@article{10_1017_S0017089515000324,
     author = {GAO, ZENGHUI and HUANG, ZHAOYONG},
     title = {WEAK {INJECTIVE} {AND} {WEAK} {FLAT} {COMPLEXES}},
     journal = {Glasgow mathematical journal},
     pages = {539--557},
     year = {2016},
     volume = {58},
     number = {3},
     doi = {10.1017/S0017089515000324},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000324/}
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