Category Theory
Zulip Server
Archive

You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.


Stream: deprecated: discrete geometry and entanglement

Topic: Moore complex


view this post on Zulip Eric Forgy (Jan 11 2021 at 20:50):

Wow. Moore complex looks very similar to how I defined a diamond complex :mind-blown:

view this post on Zulip Eric Forgy (Jan 11 2021 at 20:56):

They are definitely different, but seeing Moore complex gives me a huge hint as to a good way to define diamond complexes :+1:

view this post on Zulip Eric Forgy (Jan 11 2021 at 21:16):

https://categorytheory.zulipchat.com/#narrow/stream/266854-working.3A-discrete.20geometry.20and.20entanglement/topic/Invitation.20%28Discussion.20on.20Jan.208.20update%29/near/222242496

view this post on Zulip Eric Forgy (Jan 11 2021 at 21:20):

Kan complex

view this post on Zulip Eric Forgy (Jan 11 2021 at 22:38):

Eric Forgy said:

They are definitely different, but seeing Moore complex gives me a huge hint as to a good way to define diamond complexes :+1:

I know how to define them, but I mean that now I can define them with a presentation similar to Moore complex, which is probably worded a little more clearly than what I could come up with on my own.

view this post on Zulip Eric Forgy (Jan 11 2021 at 22:40):

It looks to me like Moore complexes are actually made up of diamonds :blush: :large_blue_diamond:

view this post on Zulip Eric Forgy (Jan 11 2021 at 22:43):

Moore complexes

view this post on Zulip Eric Forgy (Jan 11 2021 at 22:49):

Moore complexes are forward looking open cones. Diamonds are the intersection of forward and backward looking cones.

view this post on Zulip Eric Forgy (Jan 11 2021 at 22:53):

The birth of diamonds

Too bad I didn't record the exact date, but it was around (but before) Dec 21. This was one of the biggest "Eureka!" moments of my research life :nerd:

(It was definitely after Dec 18 - the previous date I marked in my notebook - and before Dec 21 - the day I sent it to a friend :blush:)

view this post on Zulip Eric Forgy (Jan 12 2021 at 08:47):

https://www.google.com/search?q=are+simplicial+sets+representable&oq=are+simplicial+sets+representable&aqs=chrome..69i57.18824j0j7&client=ms-android-samsung&sourceid=chrome-mobile&ie=UTF-8