Timeline for On the difference between a projective chain complex and a level-wise projective chain complex

Current License: CC BY-SA 3.0

13 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:57	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Aug 1, 2012 at 15:06	vote	accept	Shlomi A
Aug 1, 2012 at 13:00	comment	added	Ralph		I added a characterization of the projective objects in the non-negatively graded case. Hence each complex of projective modules that is bounded below but not exact isn't a projective object. A simple example is $\cdots \to 0 \to R \xrightarrow{r} R \to 0 \to \cdots$ where $R$ is any ring and $r$ a non-unit.
Aug 1, 2012 at 12:52	history	edited	Ralph	CC BY-SA 3.0	Added the case when the complexes are bounded below
Aug 1, 2012 at 10:39	comment	added	Shlomi A		Ralph, the question is about non-negatively graded chain complexes. In view of Ex. 1.4.1(1) in [We], if we simply cut your example in dimension 0, we get a split-exact chain complex, thus projective in $Ch_R $, thus also in $Ch_R ^\geq0$. Can this be mended to give an example of a level-wise projective chain complex which is not a projective object in $Ch_R ^\geq0$ ?
Jul 31, 2012 at 21:46	history	edited	Ralph	CC BY-SA 3.0	put the answer into a broader perspective
Jul 31, 2012 at 21:43	comment	added	Ralph		That's a good point.
Jul 31, 2012 at 13:31	vote	accept	Shlomi A
Aug 1, 2012 at 10:44
Jul 31, 2012 at 13:31	vote	accept	Shlomi A
Jul 31, 2012 at 13:31
Jul 31, 2012 at 11:37	comment	added	Fernando Muro		Let me add that this complex is a counterexample to the claim in the question's second paragraph, improperly attributed to Dwyer and Spalinski.
Jul 31, 2012 at 9:16	history	edited	Ralph	CC BY-SA 3.0	added 147 characters in body
Jul 31, 2012 at 8:48	history	edited	Ralph	CC BY-SA 3.0	added 4 characters in body
Jul 31, 2012 at 8:41	history	answered	Ralph	CC BY-SA 3.0