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Stream: deprecated: topos theory

Topic: Ionads

Oscar Cunningham (May 13 2020 at 10:15):

In Richard Garner's paper on ionads he say that (aside from size issues) one can think of the sheaves on a space $X$ as being the continuous maps $X\to\mathbf{Set}$ where $\mathbf{Set}$ has been made into an ionad using the Scott topology. But he also defines how to turn a category into a ionad using the Alexandroff topology. Does anyone know what the continuous maps $X\to\mathbf{Set}$ are when $\mathbf{Set}$ has the Alexandroff topology?

Morgan Rogers (he/him) (May 13 2020 at 14:15):

We could ask @Richard Garner, if he sees this.

Oscar Cunningham (May 13 2020 at 15:00):

Oh neat, I didn't know he was here.

Morgan Rogers (he/him) (May 13 2020 at 15:18):

I also know that @Ivan Di Liberti has worked on this topic since he presented a talk related Ionads at CT last year. (Sorry that the best I can do is invite other people to answer :joy: )

Oscar Cunningham (May 13 2020 at 15:21):

Ivan's thesis draft (https://diliberti.github.io/Research.html) has some good info on ionads (in particular it allows large ionads, contra Garner), but I don't think it answers this question

Ivan Di Liberti (Sep 05 2020 at 20:05):

I recently updated the thesis with a (almost) stable version (https://diliberti.github.io/phdthesis.pdf). By the end of the month, I hope to push something on the ArXiv. @[Mod] Morgan Rogers mentioned me a couple of times already, thus, since I have achieved a semi-stable version of it, I feel the duty of informing you.

Jens Hemelaer (Sep 05 2020 at 21:16):

Thanks for the update... I've been looking at your thesis a lot lately. I am referring to it in a work in progress so it's good to know that it will be on arxiv soon.

Ivan Di Liberti (Sep 05 2020 at 21:18):

Jens Hemelaer said:

Thanks for the update... I've been looking at your thesis a lot lately. I am referring to it in a work in progress so it's good to know that it will be on arxiv soon.

Thanks! I will write to you in private! :)

Morgan Rogers (he/him) (Sep 05 2020 at 22:59):

Congrats on getting it all together!