agda-unimath
agda-unimath copied to clipboard
Zigzag construction of identity types of pushouts
~~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 various is-section-map-inv-equivs, is-retraction-map-inv-equivs, preserves-trs etc.~~
What needs to be done:
- [x] Fill the two holes
- [ ] Factoring out general lemmas —
functoriality-stuffandstuff-overhave a lot of ad-hoc development - [ ] Naming — goes with the above
- [ ] Marking things abstract/opaque, general optimizations — the new stuff takes about as much time to typecheck as the rest of the library. I would be surprised if the CI didn't error on insufficient memory. This is fixable, but will take some time
- [ ] Prose
Ideally I'd also like to avoid relying on the computation of map-eq-transpose-equiv', which at least compute-square-over-zigzag-square-over-colimit-id does