Timeline for A canonical and categorical construction for geometric realization
Current License: CC BY-SA 2.5
5 events
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| Aug 25, 2010 at 20:24 | comment | added | Andreas Blass |
I don't think "I is an interval object in the topos $\mathcal E$" is equivalent to "Hom$(E,I)$ is an interval object in $Set$ for all $E\in\mathcal E$." Consider, for example, the case of $\mathcal E=Set$, $I=[0,1]$, and $E=2$. I don't see a linear ordering on Hom$(2,I)$ induced by the linear ordering on $I$. (This doesn't affect the rest of your answer.) Generally, this sort of "definition via Yoneda embedding" works fine for concepts defined by universal Horn sentences, but not for notions like "linear order" or "field". For these, one needs the internal logic of the topos.
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| Jun 20, 2010 at 13:57 | comment | added | David Carchedi | I've taken a brief look, but as of yet, have not penetrated too deeply. I'll let you know if I find anything of interest. Thanks for the reference! | |
| Jun 19, 2010 at 14:11 | history | edited | David Carchedi | CC BY-SA 2.5 |
typo
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| Jun 19, 2010 at 12:37 | comment | added | Steven Gubkin | Have you looked at Peter Freyd's "Algebraic Real Analysis"? I have barely cracked it open, but it seems like if you are looking for a categorical analysis of the unit interval, that is the place to go. | |
| Jun 18, 2010 at 23:45 | history | answered | David Carchedi | CC BY-SA 2.5 |