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Monoidal: convenient naturality lemmas #1944

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Alizter
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@Alizter Alizter commented May 2, 2024

The curried naturality we ask for is compact, however it makes it difficult to use in practice. These lemmas show that it is a fair bit of work to actual get the more streamlined versions out.

Split from #1929

Signed-off-by: Ali Caglayan <[email protected]>

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@Alizter Alizter requested a review from jdchristensen May 2, 2024 20:06
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Do these results follow from some more general results about naturality of curried and uncurried bifunctors?

If not, is it any easier to deduce the last three from the first one, rather than from the definition?

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Alizter commented May 2, 2024

Do these results follow from some more general results about naturality of curried and uncurried bifunctors?

Probably, but I haven't had the time to work it out. We should definitely look into it in the future.

If not, is it any easier to deduce the last three from the first one, rather than from the definition?

I'll check.

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Alizter commented May 2, 2024

Nice, it worked. The proofs are much shorter and cleaner. This will make generalising this argument to general natural transformations with 3 variables easier in the future.

@Alizter Alizter merged commit d2457d5 into HoTT:master May 3, 2024
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@Alizter Alizter deleted the ps/rr/monoidal__convenient_naturality_lemmas branch May 3, 2024 22:08
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