… theory on an additive exact category ( A , E ) . This … acyclic complex F of flat R-modules
is called totally acyclic if, … G F -phantom precover with cotorsion-flat kernel for each R -module. …

… a dualizing complex, any F-totally acyclic complex of flat right R-… of F-totally acyclic complexes
of countably presentable flat … claims that, in any acyclic complex of cotorsion modules, the …

… complete cohomology theory with respect to the cotorsion pair (W, V) … flat dimension, cotorsion
dimension, Gorenstein injective/flat dimension and projectively coresolved Gorenstein flat …

… The theory of very flat modules [61, 85], as well as our work … main concrete examples: the flat
cotorsion pair in the category … (A) containing all the absolutely acyclic complexes and closed …

… general theory of the Gorenstein flat-cotorsion dimension. … if every acyclic complex of injective
A-modules is 𝖵 -acyclic. Dually… if every acyclic complex of modules from 𝖴 is 𝖴 -acyclic and …

… say that a complex RF‚ of flat left R-modules is F-totally acyclic if RF‚ … RX‚ in ChpR-Modq is
a dg-flat resolution of RX‚ with cotorsion … flat-cotorsion if there is a totally acyclic complex of flat-…

… categories of totally acyclic complexes with applications to the flat–cotorsion theory … 119
Model structures and relative Gorenstein flat modules and chain complexes Sergio Estrada, …

… ◦ -modules and the class FC of flat and cotorsion R ◦ -modules are closed under extensions
and direct summands, and FC is a cogenerator for GF in the sense of Auslander and …

… cotorsion pairs) that wasn’t as obviously connected to the Small Object Argument, but was
crucial to the solution of the Flat … ; subcomplexes of acyclic complexes are not always acyclic!). …

… a satisfactory theory of homological dimensions of complexes … injective, and flat dimensions
for arbitrary complexes. Enochs, … and hereditary cotorsion pairs in the category of complexes …