Timeline for Sequences of maps between modules such that $\ker(d_n) \subseteq \text{im}(d_{n+1})$

8 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:19	history	edited	CommunityBot		replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
Jul 11, 2013 at 15:53	vote	accept	CommunityBot
Jul 11, 2013 at 15:53	comment	added	user32666		MO seems to have collectively answered my question at this point: probably there are no such references, because these objects are not interesting.
Apr 2, 2013 at 4:06	answer	added	Henry.L		timeline score: 2
Mar 30, 2013 at 19:13	comment	added	user32666		Fair enough. But I still think perhaps there are interesting things one might be able to say about the category of such objects (if one were to form the category of these sequences of $R$ modules, call it $\mathcal{C}$, in the natural way). For instance, is there any relationship between $\mathcal{C}$ and the category of complexes of $R$-modules? This is the sort of thing I'd like to understand. I assume questions like these have been thought about before, but I can't seem to find any references for them.
Mar 30, 2013 at 18:37	history	edited	user32666	CC BY-SA 3.0	added 69 characters in body
Mar 30, 2013 at 18:30	comment	added	Will Sawin		Every module in the sequence has two filtrations - one into the kernels of $d^k$ for increasing $k$ and one into the images of $d^k$ for decreasing $k$. There are almost no relations between these two filtrations, meaning there are a lot of isomorphism classes of these objects.
Mar 30, 2013 at 17:09	history	asked	user32666	CC BY-SA 3.0