There exists a short exact sequence of the form 0 [right arrow] A [right arrow] [T.
We obtain the short exact sequence 0 [right arrow] Ho[m.
X [right arrow] 0 is a short exact sequence of A-modules, then X [right arrow] Y [right arrow] Z is a cofibration.
n,k] and the short exact sequences relating these A -modules.
There is a characterization of Connes-amenability in terms of splitting of an admissible short exact sequence, a fact noted by Daws [5, Prop.
in terms of the approximate splitting of the short exact sequence
Also, by taking H-cohomology of the short exact sequence
Applying the Snake lemma to this diagram gives a short exact sequence
Therefore we need to show that for any short exact sequence of finite R[[x]]-modules
By taking the inverse limit of the short exact sequences
They cover complexes of modules, short exact sequences
of complexes, the category K(R-Mod), co-torsion pairs and triplets in C(R-Mod), adjoint functions, model structures, creating co-torsion pairs, minimal complexes, and Cartan and Eilenberg resolutions.
DN)--([OMEGA]) type conditions have also much to do with the splitting of short exact sequences
of Frechet spaces (see e.