Timeline for Finitely cocomplete categories of compact Hausdorff spaces
Current License: CC BY-SA 3.0
7 events
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| Jul 10, 2016 at 14:00 | comment | added | Tim Campion | A reference for the fact that every monadic category over $\mathsf{Set}$ is cocomplete can be found on the nlab, Corollary 1. Alternatively, use the observation of Linton (discussed on the same page, Theorem 1) that if $C$ is cocomplete and $C^T$ has reflexive coequalizers then $C^T$ is cocomplete. After all, compact spaces are closed under quotients, and Hausorffification is another quotient, so compact Hausdorff spaces have all coequalizers, formed by taking the coequalizer and Hausdorffifying. | |
| Mar 21, 2013 at 3:43 | vote | accept | Ricardo Andrade | ||
| Mar 19, 2013 at 9:26 | comment | added | Ricardo Andrade | @Chris: No problem. Thanks again. Also, sorry for the simple question. | |
| Mar 19, 2013 at 9:23 | history | edited | Chris Schommer-Pries | CC BY-SA 3.0 |
clarified "I"
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| Mar 19, 2013 at 9:21 | comment | added | Chris Schommer-Pries | @Ricardo: Yes I miss typed the formula the first time. It is supposed to be an upside down parabola which goes through (0,0), (0.5, 0.5) and (1, 0). I think it is fixed now. As you increase the factor 2 the behavior changes and becomes chaotic. see physics.udel.edu/~jim/PHYS460_660_13S/oscillations&chaos/… This must mean quotients become really really bad non-Hausdorff spaces. | |
| Mar 19, 2013 at 9:16 | comment | added | Ricardo Andrade | @Chris: It seems you meant $t\mapsto t^2$ or something like that. In any case, the idea stands, and I see that my conditions are way too strict. That certainly settles the question as I stated it. Thank you very much. | |
| Mar 19, 2013 at 9:06 | history | answered | Chris Schommer-Pries | CC BY-SA 3.0 |