Devalapurkar & Haine #1157
Devalapurkar & Haine #1157
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Oh wait, should I rebase on #1133? |
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Another question is, should I add the public imports in |
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This should be everything, so it's ready for review. |
| pushoutB = pushoutSquareL | ||
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| pushoutAB : PushoutSquare | ||
| pushoutAB = _ , isPushoutBottomSquare→isPushoutTotSquare (pushoutB .snd) |
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(replying to @aljungstrom on another issue) It's this line and/or possibly other similar lines. Agda is checking the middle function of the two squares agree, so that we can apply the pasting lemma. Strangely when I evaluated each field of the commSquare record they returned instantly, but it gets stuck for a couple seconds and a few GB of memory when I try to evaluate the entire record.
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See the comments slightly above for a commutative diagram of what's happening.
This is a formalization of results described in #1147, with the two main results being the stable James splitting
ΣΩΣX ≃ ΣX ⋁ Σ(X ⋀ ΩΣX)and the Hilton–Milnor splittingΩ(X ⋁ Y) ≃ ΩX × ΩY × ΩΣ(ΩY ⋀ ΩX).It still needs cleaning up and merging with #1151, but most of it is done.I'm putting the HM splitting in the Homotopy folder, but the James splitting in the HITs.James folder, because the latter result is quite related to what's already in there.