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jlh 2021-07-16 12:46:01 +01:00
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@ -57,3 +57,12 @@
- Homotopy n-types
a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
* in particular sigma types
* Debriefs
- 2021 July 15; Homotopy n-types
+ watched (Harper) lecture 15 on Sets being closed under type formations ->- motivates showing in Agda Sets closed under Sigma.
+ Harper does product case, claiming sigma case follows analogously,
+ attempt proof in Cubical Agda but highly non-obvious how to use that fibers are Sets.
+ difficulty is that PathP not in one fiber, but PathOver is, AND PathOver <-> PathP NON-obvious
+ Easy to generalize situation to n-types being closed under Sigma (7.1.8 in HoTT book), we showed this assuming PathPIsoPath
-