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jlh 2021-07-16 12:46:01 +01:00
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@ -57,3 +57,12 @@
- Homotopy n-types - Homotopy n-types
a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
* in particular sigma types * 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
-