Projects

Stream: Copenhagen Masterclass 2023

[Kevin Buzzard]

This is a summary of the various projects which people are working on during the week. I'll update it as the week progresses. Active projects should have threads associated to them in this #Copenhagen Masterclass 2023 stream.

• A sheaf on ExtrDisc is just a functor sending finite disjoint unions to finite products (talk to Filippo/Riccardo)
• Reduction of AB5 for Cond(Ab) to the above statement about sheaves on ExtrDisc (Talk to Adam)
• AB5 for the category of abelian groups (talk to David)
• Day's RP => Condensed abelian groups are closed symmetric monoidal (talk to Sina)
• Day's RP (note that there are delicate universe issues)

Finished projects:

• Adam's Tuesday lecture: coherent topology on ExtrDisc is the pullback of the coherent topology on CompHaus (talk to Nick Kuhn) (PRed!)
• Categories of sheaves of types are cartesian closed (and hence condensed sets are cartesian closed)
• A finite family of morphisms is Effective Epi iff it's jointly surjective, in Profinite / ExtrDisc (needs merging to Copenhagen repo)
• Statement of AB5 (done today in Adam lecture) (needs PRing to mathlib?)
• Profinite / ExtrDisc are precoherent (needs PRing to mathlib)
• Various inclusions ExtrDisc $\subseteq$ Profinite $\subseteq$ CompHaus are fully faithful (needs PRing to mathlib)
• Gleason's theorem: a compact Hausdorff space is projective iff it's extremally disconnected (needs PRing to mathlib)

[Riccardo Brasca]

"Profinite / ExtrDisc are precoherent" is done (but it depends on other projects)