Timeline for Why did Voevodsky consider categories "posets in the next dimension", and groupoids the correct generalisation of sets?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 1, 2018 at 8:58 | vote | accept | Soham Chowdhury | ||
| Aug 31, 2018 at 19:13 | answer | added | Mike Shulman | timeline score: 41 | |
| Aug 31, 2018 at 18:48 | comment | added | Callan McGill | In the same way an infinity groupoid might be thought of as a model for types with higher order identity relations. | |
| Aug 31, 2018 at 18:47 | comment | added | Callan McGill | If I take 0-categories as categories enriched in -1-categories i.e. truth values {0,1}, then a 0-category is equivalent to a preorder. A 0-groupoid is a 0-category in which every morphism is invertible i.e a symmetric preorder otherwise known as an equivalence relation. This means 0-groupoids are sets with equivalence relations (sometimes called setoids) which can be thought of as a set which retains evidence for equality (I believe this is the view of Bishop). The skeleton of a setoid is then the quotient (i.e. equivalence classes) which is a set. | |
| Aug 31, 2018 at 15:55 | answer | added | Giorgio Mossa | timeline score: 9 | |
| Aug 31, 2018 at 15:51 | comment | added | arsmath | I have a very low-brow answer. A poset that's a groupoid is a set with a reflexive relation on it. Conversely, you can canonically turn any set into a poset by taking its reflexive relation as the partial order. | |
| Aug 31, 2018 at 14:46 | answer | added | Ivan Di Liberti | timeline score: 12 | |
| Aug 31, 2018 at 14:20 | answer | added | Simon Henry | timeline score: 73 | |
| Aug 31, 2018 at 13:24 | history | edited | Soham Chowdhury |
a couple more tags
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| Aug 31, 2018 at 13:20 | review | First posts | |||
| Aug 31, 2018 at 13:39 | |||||
| Aug 31, 2018 at 13:19 | comment | added | Soham Chowdhury |
I had no idea what to tag this with; appropriate retagging would be appreciated. I'm not sure if this is a valid soft-question.
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| Aug 31, 2018 at 13:17 | history | asked | Soham Chowdhury | CC BY-SA 4.0 |