Ancestors

Written by Trebor on 2024-12-14 at 05:32

I seem to have come up with the universal property of the dissolution locale. If this is true then Johnstone most probably knew about it, but I don't see it written down anywhere: https://trebor-huang.github.io/forest/misc-000E.xml

=> More informations about this toot | More toots from trebor@types.pl

Toot

Written by Trebor on 2024-12-14 at 05:33

In particular the proof that the dissolution locale has the same points as the original locale is much, much clearer when phrased with the universal property

=> More informations about this toot | More toots from trebor@types.pl

Descendants

Written by Nathan Corbyn on 2024-12-14 at 07:18

@trebor I don’t understand the construction of the frame map (X -> X_d). If an open belongs to more than one closed sub-locale, where is it mapped?

=> More informations about this toot | More toots from antidote@mathstodon.xyz

Written by Trebor on 2024-12-14 at 07:21

@antidote An open is mapped to its corresponding closed sublocale, there is only one. (Some confusing order reversing is going on here, but the frame of Xd is given by the dual of the coframe of sublocales.)

=> More informations about this toot | More toots from trebor@types.pl