Towards schemes of finite presentation without size issues #1080
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
MatthiasHu
reviewed
Jan 15, 2024
| -- the Zariski lattice (classifying compact open subobjects) | ||
| private forget = ForgetfulCommAlgebra→CommRing R | ||
|
|
||
| 𝓛 : fpAlgFunctor |
There was a problem hiding this comment.
This should probably be defined by just composing the functor forget with the Z-functor version of 𝓛.
MatthiasHu
reviewed
Jan 15, 2024
| isAffine X = ∃[ A ∈ SmallFPAlgebra ] (Sp .F-ob A) ≅ᶜ X | ||
|
|
||
| -- the induced subfunctor | ||
| ⟦_⟧ᶜᵒ : {X : fpAlgFunctor} (U : CompactOpen X) → fpAlgFunctor |
There was a problem hiding this comment.
Maybe this should be defined by just taking the pullback of U and the "top element inclusion" of the lattice?
MatthiasHu
reviewed
Jan 15, 2024
| isAffineCompactOpen U = isAffine ⟦ U ⟧ᶜᵒ | ||
|
|
||
| -- the dist. lattice of compact opens | ||
| CompOpenDistLattice : Functor fpAlgFUNCTOR (DistLatticesCategory {ℓ} ^op) |
There was a problem hiding this comment.
"Homework" question for us: Can this be unified with the very similar construction of the "global sections functor" that maps X to X ⇒ 𝔸¹?
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Redoing the relevant parts of #1068 for finitely presented algebras and this time without raising universe levels.