[Merged by Bors] - feat(algebraic_geometry): Lift isomorphism of sheafed spaces to locally ringed spaces #8887
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
…unity/mathlib into split_local_ring
justus-springer
added
the
awaiting-review
2 tasks
jcommelin
approved these changes
Aug 28, 2021
Comment on lines
+106
to
+108
| Unfortunately, this equality is not well-formed, as their types are not _definitionally_ the same. | ||
| To get a proper congruence lemma, we therefore have to introduce these `eq_to_hom` arrows on | ||
| either side of the equality. |
There was a problem hiding this comment.
This is quite unfortunate. But I don't see a better solution atm.
There was a problem hiding this comment.
Yes, it took me some time to get used to all the eq_to_homs involved... But now I think it's not so bad after all.
|
✌️ justus-springer can now approve this pull request. To approve and merge a pull request, simply reply with |
github-actions
bot
added
delegated
Co-authored-by: Johan Commelin <johan@commelin.net>
…m/leanprover-community/mathlib into locally_ringed_space_reflects_iso
|
bors r+ |
bors bot
pushed a commit
that referenced
this pull request
Aug 29, 2021
…ly ringed spaces (#8887) Adds the fact that an isomorphism of sheafed spaces can be lifted to an isomorphism of locally ringed spaces. The main ingredient is the fact that stalk maps of isomorphisms are again isomorphisms. In particular, this implies that the forgetful functor `LocallyRingedSpace ⥤ SheafedSpace CommRing` reflects isomorphisms. Co-authored-by: justus-springer <50165510+justus-springer@users.noreply.github.com>
|
Pull request successfully merged into master. Build succeeded: |
bors
bot
changed the title
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.
Adds the fact that an isomorphism of sheafed spaces can be lifted to an isomorphism of locally ringed spaces. The main ingredient is the fact that stalk maps of isomorphisms are again isomorphisms.
In particular, this implies that the forgetful functor
LocallyRingedSpace ⥤ SheafedSpace CommRingreflects isomorphisms.This PR will be used to lift the isomorphism
restrict_top_isofrom the level of presheafed spaces to the level of locally ringed spaces. This is needed to complete the redefinition of Schemes (see #8888).