Timeline for Theme of Isbell duality
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Oct 14, 2014 at 7:51 | comment | added | Martin Brandenburg | I've read that objects which belong to two concrete categories at once are called schizophrenic. Usually schizophrenic objects induce adjunctions. | |
| Mar 8, 2012 at 17:39 | comment | added | Zhen Lin | You might want to be a little bit more precise about what you're saying. The reason why $\textrm{Hom}(-, \mathbb{A}^1)$ lands in the category of rings is because the theory of rings is an algebraic theory, and hence a finite limit theory a fortiori; but of course, the Yoneda embedding is left exact, so this means that each $\textrm{Hom}(S, \mathbb{A}^1)$ is a ring object in $\textbf{Set}$ in a natural way. Unfortunately this reasoning doesn't work for frames, because the theory of frames is not a finite limit theory. These objects are known as ‘dualising objects’ and some other names. | |
| Jan 12, 2012 at 12:27 | history | answered | Martin Brandenburg | CC BY-SA 3.0 |