Uniqueness of adjunction data #131
Merged
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
|
I'm a little rusty with formalization so feel free to take time reviewing this. In the meanwhile, I'll help with some of the open PRs! |
|
About to board a plane again. I'm going to work on switching the code over to the new style guide in progress. |
…d the type in which all elements are equal
|
This and #132 are now ready for review. |
fizruk
approved these changes
Oct 27, 2023
|
Good point @fizruk. Once I've actually completed of the proof of the theorem (waiting on some open issues to be finished first) I'll submit another PR with better commenting. But I'll merge this version now. |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
This essentially proves that given a functor
u : B -> Afrom a Rezk type to a Segal type, the question of whether u admits a left adjoint is a proposition.Following RS 11.23 the strategy is to prove that the type of pairs (fa, ηa) defining a transposition equivalence
hom B fa b -> hom A a (u b)is a proposition.Thus pull request stops with a proof identifying two such pairs
(fa, ηa) = (fa', ηa'). To finish I need a proof that is-equiv is a property so I'll wait for @floverity to finish with issues #56.I added a few auxiliary functions along the way, in particular reversed versions of various complicated paths, which I called
rev-name-of-original-path. I noticed in at least one instance in the library we've denoted this byname-of-original-path'so let me know if that is preferred.