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[Merged by Bors] - feat(category_theory/sites/compatible_*): Compatibility of plus and sheafification with composition. #10510

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[Merged by Bors] - feat(category_theory/sites/compatible_*): Compatibility of plus and sheafification with composition. #10510

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@adamtopaz adamtopaz commented Nov 26, 2021 •
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Compatibility of sheafification with composition. This will be used later to obtain adjunctions between categories of sheaves.

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@github-actions github-actions bot added the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Nov 26, 2021
@github-actions github-actions bot added merge-conflict Please `git merge origin/master` then a bot will remove this label. and removed blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. labels Nov 27, 2021
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🎉 Great news! Looks like all the dependencies have been resolved:

💡 To add or remove a dependency please update this issue/PR description.

Brought to you by Dependent Issues (:robot: ). Happy coding!

@github-actions github-actions bot removed the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Nov 29, 2021
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jcommelin
jcommelin reviewed Nov 29, 2021
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bors d+

src/category_theory/sites/compatible_sheafification.lean

/-- The isomorphism between the sheafification of `P` composed with `F` and
the sheafification of `P ⋙ F`. -/
def sheafify_comp_iso : J.sheafify P ⋙ F ≅ J.sheafify (P ⋙ F) :=
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Should all these defs come with simps?

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I'm not sure how useful these would be in practice. I think it would be much more useful to relate these isomorphism to sheafify_lift, but that requires additional assumptions to know that sheafification is a sheaf. What do you propose? I could add such lemmas in a separate section with these additional hypotheses, but I think simply adding simps here would generate lemmas that unfold things "too much".

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I added lemmas relating hom and inv of this construction to sheafify_lift and to to_sheafify, as well as some simp lemmas reducing the other isomorphisms in this file to these cases... take a look toward the bottom of the file.

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✌️ adamtopaz can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@github-actions github-actions bot added delegated The PR author may merge after reviewing final suggestions. and removed awaiting-review The author would like community review of the PR labels Nov 29, 2021
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bors d-

@jcommelin could you take another quick look when you have time? The last changes I made were not so trivial...

@adamtopaz adamtopaz added awaiting-review The author would like community review of the PR and removed delegated The PR author may merge after reviewing final suggestions. labels Nov 29, 2021
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Thanks 🎉

bors merge

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Nov 30, 2021
bors bot pushed a commit that referenced this pull request Nov 30, 2021
@adamtopaz
feat(category_theory/sites/compatible_*): Compatibility of plus and s…
f11d505 
…heafification with composition. (#10510)

Compatibility of sheafification with composition. This will be used later to obtain adjunctions between categories of sheaves.
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Pull request successfully merged into master.

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@bors bors bot changed the title feat(category_theory/sites/compatible_*): Compatibility of plus and sheafification with composition. [Merged by Bors] - feat(category_theory/sites/compatible_*): Compatibility of plus and sheafification with composition. Nov 30, 2021
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@bors bors bot deleted the sheafification_compatible branch November 30, 2021 07:29
jcommelin pushed a commit that referenced this pull request Dec 18, 2021
@adamtopaz @jcommelin
feat(category_theory/sites/compatible_*): Compatibility of plus and s…
baa36db 
…heafification with composition. (#10510)

Compatibility of sheafification with composition. This will be used later to obtain adjunctions between categories of sheaves.
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