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Zigzag construction of identity types of pushouts #1370
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Zigzag construction of identity types of pushouts #1370
VojtechStep
wants to merge
31
commits into
UniMath:master
from
VojtechStep:backup/wip-zigzag-construction
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I just pushed the solution to the the last hole, making this the first complete proof of correctness of the zigzag construction. 🎉 As noted in the PR description there's still quite some work necessary to make it mergeable, but the formal result is 100% there. I'll be a little self indulgent and give this the 🏆 milestone 🏆 label. |
As expected, the CI fails on insufficient memory |
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There are still two holes left to fill, but they seem to be conceptually easy enough that I'm confident publishing this draft PR now — in particular they don't have any important coherence content, and they should be provable from very general path algebra; essentially I need to (freely) give a homotopy which fits into a coherence diagram with variousis-section-map-inv-equiv
s,is-retraction-map-inv-equiv
s,preserves-tr
s etc.What needs to be done:
functoriality-stuff
andstuff-over
have a lot of ad-hoc developmentIdeally I'd also like to avoid relying on the computation of
map-eq-transpose-equiv'
, which at leastcompute-square-over-zigzag-square-over-colimit-id
does