diff --git a/Plan.org b/Plan.org index 4c87c18..d28bb8b 100644 --- a/Plan.org +++ b/Plan.org @@ -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 +-