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[Merged by Bors] - feat(category_theory/punit): A groupoid is equivalent to punit iff it has a unique arrow between any two objects #12726

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@prakol16 prakol16 commented Mar 16, 2022

In terms of topology, when this is used with the fundamental groupoid, it means that a space is simply connected (we still need to define this) if and only if any two paths between the same points are homotopic, and contractible spaces are simply connected.


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@prakol16 prakol16 changed the title feat(category_theory/groupoid): A groupoid is equivalent to punit if and only if it has a unique arrow between any two objects feat(category_theory/groupoid): A groupoid is equivalent to punit iff it has a unique arrow between any two objects Mar 16, 2022
@prakol16 prakol16 changed the title feat(category_theory/groupoid): A groupoid is equivalent to punit iff it has a unique arrow between any two objects feat(category_theory/punit): A groupoid is equivalent to punit iff it has a unique arrow between any two objects Mar 16, 2022
@prakol16 prakol16 added the awaiting-review The author would like community review of the PR label Mar 16, 2022
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Thanks! Just a few stylistic comments.

@semorrison semorrison added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Mar 16, 2022
@prakol16 prakol16 added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Mar 16, 2022
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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 Mar 16, 2022
bors bot pushed a commit that referenced this pull request Mar 17, 2022
… has a unique arrow between any two objects (#12726)

In terms of topology, when this is used with the fundamental groupoid, it means that a space is simply connected (we still need to define this) if and only if any two paths between the same points are homotopic, and contractible spaces are simply connected.
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bors bot commented Mar 17, 2022

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(category_theory/punit): A groupoid is equivalent to punit iff it has a unique arrow between any two objects [Merged by Bors] - feat(category_theory/punit): A groupoid is equivalent to punit iff it has a unique arrow between any two objects Mar 17, 2022
@bors bors bot closed this Mar 17, 2022
@bors bors bot deleted the groupoid_punit_equiv_iff_thin branch March 17, 2022 03:03
laurentbartholdi pushed a commit that referenced this pull request Mar 17, 2022
… has a unique arrow between any two objects (#12726)

In terms of topology, when this is used with the fundamental groupoid, it means that a space is simply connected (we still need to define this) if and only if any two paths between the same points are homotopic, and contractible spaces are simply connected.
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