[draft] Add definition of an adjunction in Bicategory#348
[draft] Add definition of an adjunction in Bicategory#348Boarders wants to merge 1 commit intoagda:masterfrom
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TOTBWF
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TOTBWF
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Looks good! A few minor nits, but I like where this is going 🙂.
If you are up to the task, it would be cool to prove that this is equivalent to the elementary definition in Cat like we do in Bicategory.Monad.Properties. If not, that's totally fine!
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| record Adjunction (A B : Obj) : Set (o ⊔ ℓ ⊔ e ⊔ t) where | ||
| private | ||
| module C = Extras 𝒞 |
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We should probably pull this module out of the record, and into the enclosing module.
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Yes. And may as well open it extracting the unitors and ≈.
| r-triangle-r : id₁ ⊚₀ R ⇒₂ R | ||
| r-triangle-r = C.unitorˡ.from | ||
| field | ||
| l-triangle : l-triangle-l C.≈ l-triangle-r |
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Perhaps we should name these zig and zag for alignment with Categories.Adjoint.
JacquesCarette
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JacquesCarette
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Agree with @TOTBWF : looks good, but a couple of tweaks would make it even better, and ready for inclusion.
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| record Adjunction (A B : Obj) : Set (o ⊔ ℓ ⊔ e ⊔ t) where | ||
| private | ||
| module C = Extras 𝒞 |
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Yes. And may as well open it extracting the unitors and ≈.
| r-triangle-r : id₁ ⊚₀ R ⇒₂ R | ||
| r-triangle-r = C.unitorˡ.from | ||
| field | ||
| l-triangle : l-triangle-l C.≈ l-triangle-r |
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@Boarders this was really good - a couple of small changes, and it's ready to go in. Will you be able to do there? Or would like us to? |
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@JacquesCarette Sorry for the delay, I'll be happy to get this finished soon (give me a week or so as I have a current knee injury which makes too much time at the computer somewhat tricky) |
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No worries! I'm patient and not in a hurry. Don't strain your knee for this. |
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I'd like to get this done - if you give me permission to push to your fork, I can do those small changes needed and then merge it in? |
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Hoping to get some feedback on design decisions. I am still planning to prove that this gives an equivalence in terms of hom-categories. If there is anything else that should be included feel free to let me know.