Timeline for Concise definition of subobjects
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 23, 2021 at 0:31 | comment | added | Todd Trimble | @LSpice Thanks; fixed. | |
| May 23, 2021 at 0:31 | history | edited | Todd Trimble | CC BY-SA 4.0 |
edit in response to LSpice's comment
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| Oct 16, 2014 at 9:23 | comment | added | მამუკა ჯიბლაძე | In fact one might also send both Sub (in the sense of OP) and $hom(-,\Omega)$ to categories (taking $\Omega$ to be an internal poset) and then require these two 2-functors to be equivalent (rather than isomorphic). | |
| Oct 13, 2014 at 19:36 | vote | accept | Martin Brandenburg | ||
| Oct 12, 2014 at 0:09 | comment | added | Peter LeFanu Lumsdaine | I think the well-poweredness is beside the point: the main thing is that the groupoid core of the the category of subobjects is essentially discrete, and so we are quotienting by unique isomorphisms, which is generally well-behaved. | |
| Oct 11, 2014 at 22:08 | comment | added | Todd Trimble | (I edited just as you were writing your last comment.) Yes, as I say, you're right -- it's not necessary. But it doesn't seem to be a big deal, as noted already by Anton in a comment above. | |
| Oct 11, 2014 at 22:05 | comment | added | Martin Brandenburg | (Small error: The category of subobjects is not ess. discrete ...) | |
| Oct 11, 2014 at 22:04 | history | edited | Todd Trimble | CC BY-SA 3.0 |
edited body
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| Oct 11, 2014 at 22:03 | comment | added | Martin Brandenburg | Yes, I know all this, so here are my cons: 1) Many diagrams/categories/limits are actually not small, but only essentially small. So I would define a well-powered category to be one where $\mathrm{Sub}(A)$ is essentially small for every object $A$. (Or even better, define smallness in a better non-set-theoretic way so that this becomes essentially smallness). 2) This should be seen as a functor to categories, or at least, preorders (not partial orders). | |
| Oct 11, 2014 at 21:58 | history | answered | Todd Trimble | CC BY-SA 3.0 |