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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
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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
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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
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Thanks! Just a few stylistic comments. |
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… 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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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
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… 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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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.