Timeline for Properties of right rejective subcategories
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 24, 2017 at 11:12 | comment | added | Peter LeFanu Lumsdaine | @XiaosongPeng: yep, I agree it makes sense to accept Jeremy’s answer. And yes, $\newcommand{\ker}{\mathrm{ker}}\ker_{C'} f = \ker_C f$ is another condition which would suffice here. However, the counterexample in Jeremy’s answer shows again that it doesn’t follow from the original hypotheses. | |
| Jul 24, 2017 at 1:16 | comment | added | Xiaosong Peng | @Peter LeFanu Lumsdaine Hello, Peter.If $f : X \rightarrow Y$ is a morphism in $\mathcal{C'}$. Could we get that $ker f= ker_{\mathcal{C}} f$?(here $ker_{\mathcal{C}}f$ means the kernel of $f$ viewed as morphism in $\mathcal{C}$) Another one: you and Jeremy together answered my question, I want to accept Jeremy's answer if you don't mind, is that ok? | |
| Jul 21, 2017 at 14:24 | comment | added | Jeremy Rickard | This is corrected in a later paper by Iyama. See 2.3.1 in "Representation Dimension and Solomon Zeta Function" (arxiv.org/abs/math/0308010) and the footnote on the same page. He adds the condition that $\epsilon$ is pointwise mono in $\mathcal{C}$, not just in $\mathcal{C}'$, and notes that this doesn't invalidate any applications in the previous paper. | |
| Jul 20, 2017 at 9:55 | comment | added | Peter LeFanu Lumsdaine | @XiaosongPeng: edited to add a couple of conditions. I don’t know how appropriate they are to the kind of examples this paper cares about, though. Also it’s very possible the given implication does hold as claimed without extra conditions, I’m just not seeing quite how to get that point. | |
| Jul 20, 2017 at 9:54 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 3.0 |
added some conditions implying preservation of monos
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| Jul 19, 2017 at 2:13 | comment | added | Xiaosong Peng | Thank you for your help. Are there any conditions that may induce subcategory inclusions preserve monos? | |
| Jul 18, 2017 at 14:24 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 3.0 |