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[Merged by Bors] - lint(category_theory/equivalence): docstring and a module doc #4495

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[Merged by Bors] - lint(category_theory/equivalence): docstring and a module doc #4495

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@TwoFX TwoFX commented Oct 7, 2020

@TwoFX TwoFX added awaiting-review The author would like community review of the PR lintfix This PR only fixes linting errors labels Oct 7, 2020
jcommelin
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Thanks a lot for writing this module doc!

src/category_theory/equivalence.lean Outdated
notion of "sameness" of categories than the stricter isomorphims of categories.

Our definition of equivalence includes an additional axiom, and the resulting notion of equivalence
is called a "(half-)adjoint equivalence". We show that, given an equivalence in the sense of the
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Most practicing mathematicians know what an equivalence is, and what an adjunction is. But I guess that many don't realise that there are equivalences that are not adjunctions. (I only realised this when I formalised them 😀)

Would you mind explaining in a bit more detail what the subtleties are? (Maybe part of this should even go in the docstring of equivalence, or it could have a pointer to this module docstring.)

For example, I don't know what the difference is between a half-adjoint equivalence and an adjoin equivalence. And which one does mathlib have?

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@TwoFX TwoFX Oct 7, 2020 •
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I tried to expand the explanation. Is it a bit clearer now?

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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 Oct 7, 2020
bors bot pushed a commit that referenced this pull request Oct 7, 2020
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lint(category_theory/equivalence): docstring and a module doc (#4495)
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bors bot commented Oct 7, 2020

Pull request successfully merged into master.

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@bors bors bot changed the title lint(category_theory/equivalence): docstring and a module doc [Merged by Bors] - lint(category_theory/equivalence): docstring and a module doc Oct 7, 2020
@bors bors bot closed this Oct 7, 2020
@bors bors bot deleted the lint_equivalence branch October 7, 2020 12:38
adomani pushed a commit that referenced this pull request Oct 7, 2020
@TwoFX @adomani
lint(category_theory/equivalence): docstring and a module doc (#4495)
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