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Idea: use coherently invertible maps as default notion of equivalence #946
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fredrik-bakke
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Nov 26, 2023
it would be very useful to implement #1030 before we undertake this refactoring. This will let us see if the refactoring leads to a performance improvement. |
EgbertRijke
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Feb 19, 2024
I'm ~just~ adding ~a little~ some infrastructure about coherently invertible maps ref. our discussions ~yesterday~ the other day. Don't worry, I'm not starting a huge refactoring project. Relevant to #946 and #1021. ### Summary - Add mirror file about coherence squares of homotopies after coherence squares of identifications - Add some core files for more streamlined proofs in other core files. - Refactor some proofs for coherently invertible maps - `is-emb-is-equiv` was actually a proof about coherently invertible maps - slightly improve readability of `is-coherently-invertible-is-invertible` - Prove the following (and corollaries) without "coherent replacement": - a coherently invertible map is transpose coherently invertible - the inverse of a coherently invertible map is coherently invertible - composites of coherently invertible maps are coherently invertible - coherently invertible maps are closed under homotopies
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Labels
enhancement
New feature or request
foundation
help wanted
Extra attention is needed
question
Further information is requested
refactoring
This is useful because it can give definitional computation laws for the inverse. It will take a large effort to refactor the greater library, but perhaps it is possible to start with a smaller refactoring to at least instate this as the default for future contributions. On the other hand, having two competing defaults may be detrimental to the quality and usability of the library, so we should discuss this rigorously before attempting to implement it.
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