Timeline for Pure Quotient and pure sub-object
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2013 at 0:01 | history | edited | Yemon Choi | CC BY-SA 3.0 |
I assume this is what you meant to say
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| Aug 13, 2013 at 22:18 | review | Close votes | |||
| Aug 14, 2013 at 2:17 | |||||
| Aug 13, 2013 at 19:30 | history | edited | Gholam | CC BY-SA 3.0 |
added 132 characters in body; edited tags
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| Aug 13, 2013 at 19:08 | comment | added | Tom Leinster | I suggest you edit your question to make your assumptions clear. At the moment it doesn't quite make sense, because "pure" doesn't make sense in the absence of a tensor product. As I said, that would be better than adding comments, and will make it more likely that people will answer your question. | |
| Aug 13, 2013 at 18:42 | comment | added | Gholam | Actually by the category I mean very well known categories such as the category of modules over a ring, the category of sheaves of $\mathcal{O}_X$-modules, the category of quasi-coherent sheaves, the category of representations of a quiver by a modules and etc. All of these categories are Grothendieck categories. | |
| Aug 13, 2013 at 18:12 | comment | added | Tom Leinster | So, your abelian category is assumed to have a monoidal structure too. Do you want to assume any properties of the monoidal structure (e.g. how it interacts with colimits)? I think the question would be improved if you stated your assumptions. You can edit it; that's better than adding comments or leaving answers to your own question. | |
| Aug 13, 2013 at 18:03 | answer | added | Gholam | timeline score: -2 | |
| Jul 27, 2013 at 10:07 | comment | added | Gholam | Let $\cal C$ be a category with tensor product (For example the category of modules over a ring, the category of representations of a quiver by modules, the category of sheaves of abelian groups,...). Let $$\varepsilon: 0\to A\to B\to C\to 0$$ be an exact sequence and $D$ be an arbitrary object. $\varepsilon$ is pure if The sequence $D\otimes \varepsilon$ is exact for each $D$. | |
| Jul 26, 2013 at 21:53 | comment | added | Buschi Sergio | What do you mean for "pure subobject" (pure quotient)? | |
| Jul 26, 2013 at 14:36 | history | edited | David White | CC BY-SA 3.0 |
edited title
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| Jul 26, 2013 at 13:26 | review | First posts | |||
| Jul 26, 2013 at 13:43 | |||||
| Jul 26, 2013 at 13:11 | history | asked | Gholam | CC BY-SA 3.0 |