… to complexes of modules. Gillespie [Gil04] showed that the flat cotorsion pair induces two
complete cotorsion … right minimal) if and only if so is f∗(g) in Mod A. Consequently, if f is a ring …

… complex of flat cotorsion R-modules decomposes as a direct sum of a minimal complex and
a contractible complex. … a semi-flat-cotorsion complex as a special type of semi-flat complex, …

… cotorsion flat resolutions of complexes and define and study the notion of cotorsion flat
dimension for complexes of flat R-modules… category of projective R-modules. Combined with the …

… flat cotorsion modules and minimal flat resolutions—which was developed by Enochs and Xu
for modules … shape of a dataset by building a simplicial complex on top of the dataset. This …

… We finish this chapter by proving that any complex is qùasi-isomorphic to a minimal DG-…
finitely generated module over a Gorenstein local ring. In Chapter 4 we introduce flat complexes. …

… theory over a coherent ring, this provides a new description of the category of cotorsion
Gorenstein flat modules; one that puts it on equal footing with the category of Gorenstein …

… )(R)-totally acyclic complex a totally acyclic complex of flat-cotorsion modules. The following
… In particular, R has projective dimension one as an R♯-module, with a minimal resolution …

… by the class of Gorenstein flat modules, and the fibrant objects by the class of cotorsion …
definable closure of B, that is, the smallest definable subcategory containing B. For the purposes …

… module is flat-cotorsion, we mean that it is flat and cotorsion at the same time. An acyclic
R-complex L of flat-cotorsion modules … minimal flat resolution (a flat resolution made of flat covers…

… flat complexes of flat contraadjusted modules and acyclic complexes of flat contraadjusted
modules with flat modules … of modules and complexes arise in connection with cotorsion pairs, …